Question
Solve the following problem graphically using Microsoft Excel.

Maximize Z = 8(xsub1) + 5(xsub2)

Subject to:
-4(xsub1) + xsub2 less than or equal to 1
3(xsub1) + 4(xsub2) less than or equal to 25
5(xsub1) - 2(xsub2) less than or equal to 12
-1.5(xsub1) + 3(xsub2) less than or equal to 8

and

(xsub1),(xsub2) greater than or equal to zero
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      • creating: site.headers.header (472μs)
      • composing: site.headers.header (87μs)
      • Illuminate\Cache\Events\CacheHit (1.91ms)
      • creating: components.footer (82μs)
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      • Illuminate\Cache\Events\CacheHit (900μs)
      • Illuminate\Cache\Events\CacheHit (279μs)
      • Illuminate\Cache\Events\CacheHit (262μs)
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      • Illuminate\Cache\Events\CacheHit (193μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
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      • Illuminate\Cache\Events\CacheHit (287μs)
      • Illuminate\Cache\Events\CacheHit (321μs)
      • Illuminate\Cache\Events\CacheHit (195μs)
      • Illuminate\Cache\Events\CacheHit (196μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (218μs)
      • creating: components.forms.contact-us (281μs)
      • composing: components.forms.contact-us (186μs)
      • creating: components.forms.get-started (193μs)
      • composing: components.forms.get-started (88μs)
      • creating: components.forms.free-tool-download (150μs)
      • composing: components.forms.free-tool-download (77μs)
      • creating: components.forms.claim-free-worksheet (143μs)
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      • creating: components.forms.tutor-subscription-waitlist (142μs)
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      • creating: components.forms.tutor-subscription-join (140μs)
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      • 325 x Illuminate\Cache\Events\CacheHit (15.53%)
        77.05ms
        15 x Illuminate\Database\Events\StatementPrepared (8.73%)
        43.30ms
        15 x Illuminate\Database\Events\QueryExecuted (6.43%)
        31.91ms
        3 x Illuminate\Cache\Events\KeyWritten (4.83%)
        23.95ms
        3 x Illuminate\Cache\Events\CacheMissed (2.21%)
        10.95ms
        1 x Illuminate\Foundation\Events\LocaleUpdated (0.63%)
        3.12ms
        2 x Illuminate\Database\Events\ConnectionEstablished (0.32%)
        1.59ms
        1 x Illuminate\Routing\Events\Routing (0.28%)
        1.38ms
        1 x eloquent.booting: App\Models\User\TutorAttributes\TutorDegree (0.17%)
        840μs
        1 x Illuminate\Routing\Events\RouteMatched (0.11%)
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        527μs
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        511μs
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        472μs
        1 x creating: components.breadcrumbs (0.08%)
        420μs
        1 x creating: homework.show (0.07%)
        354μs
        7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.07%)
        332μs
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        299μs
        1 x eloquent.booting: App\Models\SubjectCat (0.06%)
        298μs
        1 x creating: components.forms.contact-us (0.06%)
        281μs
        1 x composing: components.breadcrumbs (0.05%)
        251μs
        1 x creating: components.open-graph (0.05%)
        242μs
        2 x eloquent.retrieved: App\Models\SubjectCat (0.05%)
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        222μs
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        178μs
        3 x eloquent.retrieved: App\Models\User\Tutor (0.03%)
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        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.03%)
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        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.03%)
        164μs
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        160μs
        1 x eloquent.booted: App\Models\User\Tutor (0.03%)
        156μs
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        150μs
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        143μs
        1 x creating: components.forms.tutor-subscription-waitlist (0.03%)
        142μs
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        142μs
        1 x creating: components.forms.tutor-subscription-join (0.03%)
        140μs
        1 x composing: components.canonical (0.02%)
        117μs
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        98μs
        1 x eloquent.booting: App\Models\User\Tutor (0.02%)
        90μs
        1 x composing: components.forms.get-started (0.02%)
        88μs
        1 x composing: components.forms.tutor-subscription-join (0.02%)
        88μs
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        87μs
        1 x composing: components.open-graph (0.02%)
        86μs
        1 x creating: components.footer (0.02%)
        82μs
        1 x composing: components.forms.tutor-support (0.02%)
        79μs
        1 x composing: components.forms.free-tool-download (0.02%)
        77μs
        1 x composing: components.forms.claim-free-worksheet (0.02%)
        77μs
        1 x composing: components.forms.tutor-subscription-waitlist (0.02%)
        76μs
        1 x eloquent.booting: App\Models\Subject (0.01%)
        56μs
        1 x eloquent.booted: App\Models\User\TutorAttributes\TutorDegree (0.01%)
        48μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.01%)
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      • 1x homework.showshow.blade.phpblade
      • 1x components.breadcrumbsbreadcrumbs.blade.phpblade
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      • 1x site.headers.headerheader.blade.phpblade
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      • 1x components.forms.get-startedget-started.blade.phpblade
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      • 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
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      app/Http/Controllers/HomeworkLibraryController.php:79-176
      15 statements were executed, 4 of which were duplicates, 11 unique. Show only duplicated60.78ms
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        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` = '20492' limit 1
        19.78mstwenty4_siteHomeworkLibraryController.php#97
        Bindings
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        • 1: 0
        • 2: 20492
        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 (73)
        1.17mstwenty4_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 (20492)
        3.09mstwenty4_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` = 1 limit 1
        1.01mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 1
        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
      • Connection Establishedtwenty4_siteHomeworkLibraryController.php#124
        Backtrace
        • 13. app/Http/Controllers/HomeworkLibraryController.php:124
        • 14. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 15. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 17. app/Http/Controllers/HomeworkLibraryController.php:136
        • 18. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • select * from `users` where `disable_profile` = 0 and `picture` != '' and `solutionrequestQualified` = 1 and `is_suspended` = 0 and `is_deactivated` = 0 and `status` != '' and `status` = 'tutor' order by `completed_requests` desc limit 3
        22.14mstwenty4_siteHomeworkLibraryController.php#128
        Bindings
        • 0: 0
        • 1: 
        • 2: 1
        • 3: 0
        • 4: 0
        • 5: 
        • 6: tutor
        Backtrace
        • 14. app/Http/Controllers/HomeworkLibraryController.php:128
        • 15. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 16. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 18. app/Http/Controllers/HomeworkLibraryController.php:136
        • 19. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • select * from `tutor_degrees` where `tutor_degrees`.`tutor_id` = 6002 and `tutor_degrees`.`tutor_id` is not null order by `year` desc limit 1
        1.11mstwenty4_siteTutor.php#361
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        Backtrace
        • 18. app/Models/User/Tutor.php:361
        • 19. app/Transformers/Tutor/TutorTransformer.php:74
        • 22. vendor/league/fractal/src/TransformerAbstract.php:128
        • 23. vendor/league/fractal/src/TransformerAbstract.php:107
        • 24. vendor/league/fractal/src/Scope.php:383
      • select * from `tutor_degrees` where `tutor_degrees`.`tutor_id` = 2821 and `tutor_degrees`.`tutor_id` is not null order by `year` desc limit 1
        940μstwenty4_siteTutor.php#361
        Bindings
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        Backtrace
        • 18. app/Models/User/Tutor.php:361
        • 19. app/Transformers/Tutor/TutorTransformer.php:74
        • 22. vendor/league/fractal/src/TransformerAbstract.php:128
        • 23. vendor/league/fractal/src/TransformerAbstract.php:107
        • 24. vendor/league/fractal/src/Scope.php:383
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        1.24mstwenty4_siteTutor.php#361
        Bindings
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        Backtrace
        • 18. app/Models/User/Tutor.php:361
        • 19. app/Transformers/Tutor/TutorTransformer.php:74
        • 22. vendor/league/fractal/src/TransformerAbstract.php:128
        • 23. vendor/league/fractal/src/TransformerAbstract.php:107
        • 24. vendor/league/fractal/src/Scope.php:383
      • select * from `solutionslibrary` where `id` <> 20492 and `subject` = 73 and `status` = 'published' and `price` > 0 order by RAND() limit 6
        3.21mstwenty4_siteHomeworkLibraryRepository.php#30
        Bindings
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        • 1: 73
        • 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 (73)
        1.13mstwenty4_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` = 20492 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        1.21mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 20492
        • 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` = 20492 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'teaser' order by `order` asc, `id` asc
        860μstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 20492
        • 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` = 20492 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'solution' order by `order` asc, `id` asc
        1.6mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 20492
        • 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 count(*) as aggregate from `users` where `disable_profile` = 0 and `picture` != '' and `solutionrequestQualified` = 1 and `is_suspended` = 0 and `is_deactivated` = 0 and `status` != '' and `status` = 'tutor'
        1.29mstwenty4_siteTutor.php#479
        Bindings
        • 0: 0
        • 1: 
        • 2: 1
        • 3: 0
        • 4: 0
        • 5: 
        • 6: tutor
        Backtrace
        • 15. app/Models/User/Tutor.php:479
        • 16. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 17. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 19. app/Models/User/Tutor.php:480
        • 20. app/Http/Controllers/HomeworkLibraryController.php:169
      • select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1
        1mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 1
        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
      App\Models\HomeworkLibrary\HomeworkLibrary
      7HomeworkLibrary.php
      App\Models\HomeworkLibrary\HomeworkLibraryFile
      5HomeworkLibraryFile.php
      App\Models\User\Tutor
      3Tutor.php
      App\Models\Subject
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      App\Models\SubjectCat
      2SubjectCat.php
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          request_cookies
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