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Linear Programming Sherwood Furniture Company Recently, Sherwood Furniture Company has been interested in developing a new line of stereo speaker cabinets.

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Presentation on theme: "Linear Programming Sherwood Furniture Company Recently, Sherwood Furniture Company has been interested in developing a new line of stereo speaker cabinets."— Presentation transcript:

1 Linear Programming Sherwood Furniture Company Recently, Sherwood Furniture Company has been interested in developing a new line of stereo speaker cabinets. In the coming month, Sherwood expects to have excess capacity in its Assembly and Finishing departments and would like to experiment with two new models. One model is the Standard, a large, high-quality cabinet in a traditional design that can be sold in virtually unlimited quantities to several manufacturers of audio equipment. The other model is the Custom, a small, inexpensive cabinet in a novel design that a single buyer will purchase on an exclusive basis. Under the tentative terms of this agreement, the buyer will purchase as many Customs as Sherwood produces, up to 32 units. The Standard requires 4 hours in the Assembly Department and 8 hours in the Finishing Department, and each unit contributes $20 to profit. The Custom requires 3 hours in Assembly and 2 hours in Finishing, and each unit contributes $10 to profit. Current plans call for 120 hours to be available next month in Assembly and 160 hours in Finishing for cabinet production, and Sherwood desires to allocate this capacity in the most economical way.

2 Linear Programming Sherwood Furniture Company – Linear Equations

3 Linear Programming Sherwood Furniture Company – Graph Solution

4 Linear Programming Sherwood Furniture Company – Graph Solution Constraint 1

5 Linear Programming Sherwood Furniture Company – Graph Solution Constraint 1

6 Linear Programming Sherwood Furniture Company – Graph Solution Constraint 2

7 Linear Programming Sherwood Furniture Company – Graph Solution Constraint 1 & 2

8 Linear Programming Sherwood Furniture Company – Graph Solution Constraint 3

9 Linear Programming Sherwood Furniture Company – Graph Solution Constraint 1, 2 & 3

10 Linear Programming Sherwood Furniture Company – Graph Solution

11 Linear Programming Sherwood Furniture Company – Graph Solution

12 Linear Programming Sherwood Furniture Company – Solve Linear Equations

13 Linear Programming Sherwood Furniture Company – Solve Linear Equations

14 Linear Programming Sherwood Furniture Company – Solve Linear Equations

15 Linear Programming Sherwood Furniture Company – Graph Solution Optimal Point (15, 20)

16 Linear Programming Sherwood Furniture Company – Slack Calculation

17 Linear Programming Sherwood Furniture Company - Slack Variables Max 20x x 2 + 0S 1 + 0S 2 + 0S 3 s.t. 4x 1 + 3x 2 + 1S 1 = 120 8x 1 + 2x 2 + 1S 2 = 160 x 2 + 1S 3 = 32 x 1, x 2, S 1,S 2,S 3 >= 0

18 Linear Programming Sherwood Furniture Company – Graph Solution 2 3 1

19 Linear Programming Sherwood Furniture Company – Slack Calculation Point 1 Point 1

20 Linear Programming Sherwood Furniture Company – Graph Solution 2 3 1

21 Linear Programming Sherwood Furniture Company – Slack Calculation Point 2 Point 2

22 Linear Programming Sherwood Furniture Company – Graph Solution 2 3 1

23 Linear Programming Sherwood Furniture Company – Slack Calculation Point 3 Point 3

24 Linear Programming Sherwood Furniture Company – Slack Calculation Points 1, 2 & 3 Point 1Point 2Point 3

25 Linear Programming Sherwood Furniture Company – Slack Variables For each ≤ constraint the difference between the RHS and LHS (RHS-LHS). It is the amount of resource left over.  Constraint 1; S 1 = 0 hrs.  Constraint 2; S 2 = 0 hrs.  Constraint 3; S 3 = 12 Custom


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