1. 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.
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2. Sherwood Furniture Company – Linear Equations
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3. Sherwood Furniture Company – Graph Solution
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4. Sherwood Furniture Company – Graph Solution Constraint 1
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5. Sherwood Furniture Company – Graph Solution Constraint 1
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6. Sherwood Furniture Company – Graph Solution Constraint 2
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7. Sherwood Furniture Company – Graph Solution Constraint 1 & 2
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8. Sherwood Furniture Company – Graph Solution Constraint 3
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9. Sherwood Furniture Company – Graph Solution Constraint 1, 2 & 3
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10. Sherwood Furniture Company – Graph Solution
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11. Sherwood Furniture Company – Graph Solution
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12. Sherwood Furniture Company – Solve Linear Equations
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13. Sherwood Furniture Company – Solve Linear Equations
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14. Sherwood Furniture Company – Solve Linear Equations
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15. Sherwood Furniture Company – Graph Solution
Optimal Point
(15, 20)
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16. Sherwood Furniture Company – Slack Calculation
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17. Sherwood Furniture Company - Slack Variables
Max
20x1 + 10x2 + 0S1 + 0S2 + 0S3
s.t.
4x x2 + 1S = 120
8x x S = 160
x S3 = 32
x1, x2, S1 ,S2 ,S3 >= 0
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18. Sherwood Furniture Company – Graph Solution3 1 2
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19. Sherwood Furniture Company – Slack Calculation Point 1
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20. Sherwood Furniture Company – Graph Solution3 1 2
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21. Sherwood Furniture Company – Slack Calculation Point 2
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22. Sherwood Furniture Company – Graph Solution3 1 2
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23. Sherwood Furniture Company – Slack Calculation Point 3
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24. Sherwood Furniture Company – Slack Calculation Points 1, 2 & 3
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25. 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; S1 = 0 hrs.
Constraint 2; S2 = 0 hrs.
Constraint 3; S3 = 12 Custom
Linear Programming