You are the operating manager of a symphony, a non-profit entity....

Question
You are the operating manager of a symphony, a non-profit entity. Your symphony hall can seat 500 people for any given performance. You figure an overhead charge of $2,800 per performance. The marginal cost of an additional patron is $6 (cleaning and ushers). You estimate that demand is P = 60 - .1Q^D

a) List possible goals for the symphony. Discuss the merits of each goal.
b) Draw your revenue and costs (MC, AVC, and AC). Do the same for demand and marginal revenue.
c) Discuss what price you will set (with regard to your goal stated in part a). You should also consider what prices you should set under other possible goals. What is profit under different options?
d) Suppose you are a sales representative, who is paid strictly on commission (4% of ticket revenues), attending the pricing meeting. What (self-interested) price would you advise?
e) Suppose you get a corporate sponsor to cover $1,000 of overhead per event. How would this affect your answers?

What I do know (I think) but trying to tie this all together:

MC=$6
Demand curve = P=60-.1Q^D
MR = 60-.2Q=6
Q=260

P=60-.1(260) = 24

Symphony would produce $26/ticket (60-34)

Would somehow 2800/500 = $5.60 be involved and .40 as profit function?
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(a) There can be three possible goals for the firm and these are profit maximization, revenue maximization and sales maximization. In the profit maximization goal the symphony firm can achieve maximum profits at a point of MC=MR. Similarly with the revenue maximization goal, the firm can earn maximum revenue but the profits would be much lower. In the sales maximization goal, the firm would be able to sell its maximum capacity of seats as it cannot accommodate more than the 500 seats available per event.

AR=P = 60-0.1Q
TR= P*Q = 60Q-0.1Q²
MR = 60 - 0.2Q
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      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (252μs)
      • Illuminate\Cache\Events\CacheHit (253μs)
      • Illuminate\Cache\Events\CacheHit (345μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheMissed (278μs)
      • Illuminate\Database\Events\StatementPrepared (797μs)
      • Illuminate\Database\Events\QueryExecuted (963μs)
      • eloquent.retrieved: App\Models\SubjectCat (59μs)
      • Illuminate\Cache\Events\KeyWritten (398μs)
      • Illuminate\Cache\Events\CacheHit (1ms)
      • Illuminate\Cache\Events\CacheHit (210μs)
      • Illuminate\Cache\Events\CacheHit (162μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (777μs)
      • Illuminate\Cache\Events\CacheHit (246μs)
      • Illuminate\Cache\Events\CacheHit (498μs)
      • Illuminate\Cache\Events\CacheHit (447μs)
      • Illuminate\Cache\Events\CacheHit (259μs)
      • Illuminate\Cache\Events\CacheHit (186μs)
      • Illuminate\Cache\Events\CacheHit (218μs)
      • Illuminate\Cache\Events\CacheHit (233μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (157μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
      • creating: site.layouts.app (508μs)
      • composing: site.layouts.app (28μs)
      • creating: components.canonical (803μs)
      • composing: components.canonical (105μs)
      • creating: components.open-graph (208μs)
      • composing: components.open-graph (78μs)
      • creating: site.headers.header (313μs)
      • composing: site.headers.header (77μs)
      • Illuminate\Cache\Events\CacheHit (2.53ms)
      • creating: components.footer (83μs)
      • composing: components.footer (97μs)
      • Illuminate\Cache\Events\CacheHit (1.25ms)
      • Illuminate\Cache\Events\CacheMissed (476μs)
      • Illuminate\Database\Events\StatementPrepared (1.26ms)
      • Illuminate\Database\Events\QueryExecuted (1.31ms)
      • eloquent.retrieved: App\Models\SubjectCat (114μs)
      • Illuminate\Cache\Events\KeyWritten (419μs)
      • Illuminate\Cache\Events\CacheHit (389μs)
      • Illuminate\Cache\Events\CacheHit (1.18ms)
      • Illuminate\Cache\Events\CacheHit (264μs)
      • Illuminate\Cache\Events\CacheHit (586μs)
      • Illuminate\Cache\Events\CacheHit (363μs)
      • Illuminate\Cache\Events\CacheHit (308μs)
      • Illuminate\Cache\Events\CacheHit (1.01ms)
      • Illuminate\Cache\Events\CacheHit (274μs)
      • Illuminate\Cache\Events\CacheHit (293μs)
      • Illuminate\Cache\Events\CacheHit (440μs)
      • Illuminate\Cache\Events\CacheHit (242μs)
      • Illuminate\Cache\Events\CacheHit (1.12ms)
      • creating: components.forms.contact-us (522μs)
      • composing: components.forms.contact-us (462μs)
      • creating: components.forms.get-started (518μs)
      • composing: components.forms.get-started (86μs)
      • creating: components.forms.free-tool-download (180μs)
      • composing: components.forms.free-tool-download (117μs)
      • creating: components.forms.claim-free-worksheet (258μs)
      • composing: components.forms.claim-free-worksheet (83μs)
      • creating: components.forms.tutor-subscription-waitlist (122μs)
      • composing: components.forms.tutor-subscription-waitlist (62μs)
      • creating: components.forms.tutor-subscription-join (116μs)
      • composing: components.forms.tutor-subscription-join (195μs)
      • creating: components.forms.tutor-support (141μs)
      • composing: components.forms.tutor-support (68μs)
      • 311 x Illuminate\Cache\Events\CacheHit (17.96%)
        109ms
        20 x Illuminate\Database\Events\QueryExecuted (8.1%)
        49.26ms
        20 x Illuminate\Database\Events\StatementPrepared (4.65%)
        28.28ms
        11 x Illuminate\Cache\Events\KeyWritten (1.8%)
        10.94ms
        11 x Illuminate\Cache\Events\CacheMissed (1.68%)
        10.25ms
        1 x Illuminate\Foundation\Events\LocaleUpdated (0.75%)
        4.56ms
        12 x eloquent.retrieved: App\Models\SubjectCat (0.29%)
        1.74ms
        1 x Illuminate\Routing\Events\Routing (0.27%)
        1.63ms
        1 x Illuminate\Database\Events\ConnectionEstablished (0.21%)
        1.25ms
        1 x creating: components.breadcrumbs (0.2%)
        1.19ms
        1 x creating: components.canonical (0.13%)
        803μs
        2 x eloquent.retrieved: App\Models\Subject (0.13%)
        779μs
        1 x Illuminate\Routing\Events\RouteMatched (0.12%)
        732μs
        1 x eloquent.booting: App\Models\SubjectCat (0.11%)
        650μs
        1 x creating: components.forms.contact-us (0.09%)
        522μs
        1 x creating: components.forms.get-started (0.09%)
        518μs
        1 x creating: site.layouts.app (0.08%)
        508μs
        1 x composing: components.forms.contact-us (0.08%)
        462μs
        1 x creating: homework.show (0.07%)
        440μs
        7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.06%)
        343μs
        1 x creating: site.headers.header (0.05%)
        313μs
        1 x eloquent.booting: App\Models\Subject (0.05%)
        288μs
        1 x creating: components.forms.claim-free-worksheet (0.04%)
        258μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.04%)
        229μs
        1 x composing: components.breadcrumbs (0.04%)
        227μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.03%)
        210μs
        1 x creating: components.open-graph (0.03%)
        208μs
        1 x composing: components.forms.tutor-subscription-join (0.03%)
        195μs
        1 x creating: components.forms.free-tool-download (0.03%)
        180μs
        6 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.03%)
        179μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.03%)
        160μs
        1 x composing: homework.show (0.03%)
        159μs
        1 x creating: components.forms.tutor-support (0.02%)
        141μs
        1 x creating: components.forms.tutor-subscription-waitlist (0.02%)
        122μs
        1 x composing: components.forms.free-tool-download (0.02%)
        117μs
        1 x creating: components.forms.tutor-subscription-join (0.02%)
        116μs
        1 x composing: components.canonical (0.02%)
        105μs
        1 x composing: components.footer (0.02%)
        97μs
        1 x composing: components.forms.get-started (0.01%)
        86μs
        1 x creating: components.footer (0.01%)
        83μs
        1 x composing: components.forms.claim-free-worksheet (0.01%)
        83μs
        1 x composing: components.open-graph (0.01%)
        78μs
        1 x composing: site.headers.header (0.01%)
        77μs
        1 x composing: components.forms.tutor-support (0.01%)
        68μs
        1 x eloquent.booted: App\Models\Subject (0.01%)
        65μs
        1 x eloquent.booted: App\Models\SubjectCat (0.01%)
        64μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.01%)
        62μs
        1 x composing: components.forms.tutor-subscription-waitlist (0.01%)
        62μs
        1 x composing: site.layouts.app (0%)
        28μs
      14 templates were rendered
      • 1x homework.showshow.blade.phpblade
      • 1x components.breadcrumbsbreadcrumbs.blade.phpblade
      • 1x site.layouts.appapp.blade.phpblade
      • 1x components.canonicalcanonical.blade.phpblade
      • 1x components.open-graphopen-graph.blade.phpblade
      • 1x site.headers.headerheader.blade.phpblade
      • 1x components.footerfooter.blade.phpblade
      • 1x components.forms.contact-uscontact-us.blade.phpblade
      • 1x components.forms.get-startedget-started.blade.phpblade
      • 1x components.forms.free-tool-downloadfree-tool-download.blade.phpblade
      • 1x components.forms.claim-free-worksheetclaim-free-worksheet.blade.phpblade
      • 1x components.forms.tutor-subscription-waitlisttutor-subscription-waitlist.blade.phpblade
      • 1x components.forms.tutor-subscription-jointutor-subscription-join.blade.phpblade
      • 1x components.forms.tutor-supporttutor-support.blade.phpblade
      uri
      GET college-homework-library/{category}/{subject}/{id}
      middleware
      web, utm.parameters
      controller
      App\Http\Controllers\HomeworkLibraryController@show
      namespace
      where
      as
      homework.show
      file
      app/Http/Controllers/HomeworkLibraryController.php:79-176
      20 statements were executed, 5 of which were duplicates, 15 unique. Show only duplicated54.92ms
      • Connection Establishedtwenty4_siteHomeworkLibraryController.php#91
        Backtrace
        • 13. app/Http/Controllers/HomeworkLibraryController.php:91
        • 14. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 15. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 16. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `solutionslibrary` where `status` = 'published' and `price` > 0 and `solutionslibrary`.`id` = '47518' limit 1
        8.32mstwenty4_siteHomeworkLibraryController.php#97
        Bindings
        • 0: published
        • 1: 0
        • 2: 47518
        Backtrace
        • 16. app/Http/Controllers/HomeworkLibraryController.php:97
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 18. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 19. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 20. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subjects` where `subjects`.`id` in (20)
        1.19mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` in (47518)
        2.22mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subject_cats` where `subject_cats`.`id` = 4 limit 1
        1.03mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 4
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 26. app/Http/Controllers/HomeworkLibraryController.php:105
        • 27. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 28. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 29. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
      • select * from `solutionslibrary` where `id` <> 47518 and `subject` = 20 and `status` = 'published' and `price` > 0 order by RAND() limit 6
        19.96mstwenty4_siteHomeworkLibraryRepository.php#30
        Bindings
        • 0: 47518
        • 1: 20
        • 2: published
        • 3: 0
        Backtrace
        • 14. app/Repositories/HomeworkLibraryRepository.php:30
        • 15. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 16. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 18. app/Repositories/HomeworkLibraryRepository.php:39
        • 19. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `subjects` where `subjects`.`id` in (20)
        1.09mstwenty4_siteHomeworkLibraryRepository.php#30
        Backtrace
        • 19. app/Repositories/HomeworkLibraryRepository.php:30
        • 20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 21. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 23. app/Repositories/HomeworkLibraryRepository.php:39
        • 24. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 47518 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        1.3mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 47518
        • 1: question
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:58
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 47518 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'teaser' order by `order` asc, `id` asc
        4.41mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 47518
        • 1: teaser
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:69
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 47518 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'solution' order by `order` asc, `id` asc
        1.15mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 47518
        • 1: solution
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:80
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `subject_cats` where `subject_cats`.`id` = 4 limit 1
        1.04mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 4
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 32. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 33. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 34. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
        • 35. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1
        1.62mstwenty4_siteSubject.php#100
        Bindings
        • 0: 1
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 3 limit 1
        1.29mstwenty4_siteSubject.php#100
        Bindings
        • 0: 3
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 4 limit 1
        1.26mstwenty4_siteSubject.php#100
        Bindings
        • 0: 4
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 10 limit 1
        1.16mstwenty4_siteSubject.php#100
        Bindings
        • 0: 10
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 33 limit 1
        1.1mstwenty4_siteSubject.php#100
        Bindings
        • 0: 33
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 11 limit 1
        1.44mstwenty4_siteSubject.php#100
        Bindings
        • 0: 11
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 5 limit 1
        1.39mstwenty4_siteSubject.php#100
        Bindings
        • 0: 5
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 34 limit 1
        1.07mstwenty4_siteSubject.php#100
        Bindings
        • 0: 34
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 31 limit 1
        1.1mstwenty4_siteSubject.php#100
        Bindings
        • 0: 31
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 36 limit 1
        1.78mstwenty4_siteSubject.php#100
        Bindings
        • 0: 36
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 28. view::components.footer:170
      App\Models\SubjectCat
      12SubjectCat.php
      App\Models\HomeworkLibrary\HomeworkLibrary
      7HomeworkLibrary.php
      App\Models\HomeworkLibrary\HomeworkLibraryFile
      6HomeworkLibraryFile.php
      App\Models\Subject
      2Subject.php
          _token
          EC4bZqulvtXupaK1OU9O5MQv8uRO194q9YAIHLo1
          utm_source
          direct
          redirectUrl
          /college-homework-library/Business/Economics/47518
          _previous
          array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Business/Econom...
          _flash
          array:2 [ "old" => [] "new" => [] ]
          PHPDEBUGBAR_STACK_DATA
          []
          path_info
          /college-homework-library/Business/Economics/47518
          status_code
          200
          
          status_text
          OK
          format
          html
          content_type
          text/html; charset=UTF-8
          request_query
          []
          
          request_request
          []
          
          request_headers
          0 of 0
          array:21 [ "priority" => array:1 [ 0 => "u=0, i" ] "accept-encoding" => array:1 [ 0 => "gzip, deflate, br, zstd" ] "sec-fetch-dest" => array:1 [ 0 => "document" ] "sec-fetch-user" => array:1 [ 0 => "?1" ] "sec-fetch-mode" => array:1 [ 0 => "navigate" ] "sec-fetch-site" => array:1 [ 0 => "none" ] "accept" => array:1 [ 0 => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" ] "user-agent" => array:1 [ 0 => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" ] "upgrade-insecure-requests" => array:1 [ 0 => "1" ] "sec-ch-ua-platform" => array:1 [ 0 => ""Windows"" ] "sec-ch-ua-mobile" => array:1 [ 0 => "?0" ] "sec-ch-ua" => array:1 [ 0 => ""HeadlessChrome";v="129", "Not=A?Brand";v="8", "Chromium";v="129"" ] "cache-control" => array:1 [ 0 => "no-cache" ] "pragma" => array:1 [ 0 => "no-cache" ] "x-amzn-trace-id" => array:1 [ 0 => "Root=1-6805c14e-6e711222487c71ad277cc73c" ] "host" => array:1 [ 0 => "staging.dev.24houranswers.com" ] "x-forwarded-port" => array:1 [ 0 => "443" ] "x-forwarded-proto" => array:1 [ 0 => "https" ] "x-forwarded-for" => array:1 [ 0 => "3.133.100.195" ] "content-length" => array:1 [ 0 => "" ] "content-type" => array:1 [ 0 => "" ] ]
          request_cookies
          []
          
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