Recently, Sherwood Furniture Company has been interested i

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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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Sherwood Furniture Company Linear Equations
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Sherwood Furniture Company Graph Solution
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Sherwood Furniture Company Graph Solution
Constraint 1
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Sherwood Furniture Company Graph Solution
Constraint 1
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Sherwood Furniture Company Graph Solution
Constraint 2
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Sherwood Furniture Company Graph Solution
Constraint 1 2
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Sherwood Furniture Company Graph Solution
Constraint 3
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Sherwood Furniture Company Graph Solution
Constraint 1, 2 3
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Sherwood Furniture Company Graph Solution
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Sherwood Furniture Company Graph Solution
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Sherwood Furniture Company Solve Linear
Equations
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Sherwood Furniture Company Solve Linear
Equations
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Sherwood Furniture Company Solve Linear
Equations
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Sherwood Furniture Company Graph Solution
Optimal Point (15, 20)
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Sherwood Furniture Company Slack Calculation
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Sherwood Furniture Company - Slack Variables

• Max
• 20x1 10x2 0S1 0S2 0S3
• s.t.
• 4x1 3x2 1S1
  120
• 8x1 2x2 1S2
  160
• x2 1S3 32
• x1, x2, S1 ,S2 ,S3 gt 0

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Sherwood Furniture Company Graph Solution
3
2
1
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Sherwood Furniture Company Slack Calculation
Point 1
Point 1
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Sherwood Furniture Company Graph Solution
3
2
1
21
Sherwood Furniture Company Slack Calculation
Point 2
Point 2
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Sherwood Furniture Company Graph Solution
3
2
1
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Sherwood Furniture Company Slack Calculation
Point 3
Point 3
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Sherwood Furniture Company Slack Calculation
Points 1, 2 3
Point 1
Point 2
Point 3
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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