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# Whether to produce desks, tables, or chairs

Best Answer BobbyGo, 17 May 2013 - 07:54 PM

If you're interested, I ran a bit of code to find the answer...

Spoiler for

Go to the full post

9 replies to this topic

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Posted 17 May 2013 - 02:49 AM

Resource                 Desk                           Table                        Chair                          Availability

Lumber                    8 board ft                    6 board ft                 1 board ft                    48 board ft

Finishing                  4 hours                       2 hours                    1.5 hours                     20 hours

Carpentry                 2 hours                      1.5 hours                  0.5 hours                    8 hours

Selling Price             \$60                            \$30                           \$20

Given the constraints listed in terms of time and wood available, how many of each object should be produced to maximize revenue?

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Posted 17 May 2013 - 03:07 AM

Spoiler for SETUP

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Posted 17 May 2013 - 03:27 AM

Spoiler for SETUP

You don't need to use all just find the optimal solution

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Posted 17 May 2013 - 03:30 AM

Spoiler for SETUP

You don't need to use all just find the optimal solution

That's why I just called it "setup"; I ran it with = instead of <=, and that yielded a clearly nonsensical solution, so I included that note.

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Posted 17 May 2013 - 03:35 AM

Spoiler for SETUP

You don't need to use all just find the optimal solution

That's why I just called it "setup"; I ran it with = instead of <=, and that yielded a clearly nonsensical solution, so I included that note.

My apologies, sometimes my english isn't the best.

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Posted 17 May 2013 - 03:37 AM

Spoiler for SETUP

You don't need to use all just find the optimal solution

That's why I just called it "setup"; I ran it with = instead of <=, and that yielded a clearly nonsensical solution, so I included that note.

My apologies, sometimes my english isn't the best.

No problem, just clarifying that that wasn't an answer, just providing the initial setup

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### #7 dark_magician_92

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Posted 17 May 2013 - 12:17 PM

don't know how to solve 3 variable inequalities but
Spoiler for

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Posted 17 May 2013 - 04:33 PM

don't know how to solve 3 variable inequalities but

Spoiler for

Spoiler for Eliminating solution method

EDIT:

Spoiler for more notes, still not solution

Edited by ShadowAngel7, 17 May 2013 - 04:43 PM.

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### #9 BobbyGo

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Posted 17 May 2013 - 07:54 PM   Best Answer

If you're interested, I ran a bit of code to find the answer...

Spoiler for

Edited by BobbyGo, 17 May 2013 - 07:55 PM.

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Posted 17 May 2013 - 11:26 PM

If you wanted to do it manually, i included a screenshot using the direct "enter the basis approach" (utilizing linear algebra)

so where you see the ones in the columns among the zeroes is the 'solutions'  Z value is on top that is the maximum revenue, find the x1 score of one then read all the way across to find its quantity, etc.  You will notice the extra variables (s1, s2, s3)  these variables are the slack variables, that is the extra resources that will be left even in the optimal situation.  IN this case s1 (the amount of boards will have leftovers) but the other two constraints will be fully exhausted

Edited by BMAD, 17 May 2013 - 11:33 PM.

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