Question

The profit function for two products is Profit = -3x,? + 42x4 - 3x2? + 46x2 + 700, where x, represents units of production of

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Answer #1

(a)

Optimization model is following:

2 Max -3x1 + 42X1 – 3x2 + 46x2 + 700 – 50T s.t. 4x1 + 6x2 < 24 + OT X1, X2, OT 20

(b)

Set up Excel model as follows:

А B с D E 1 2 Units of product 1 x1 = 3 Units of product 2 x2 = 4 Overtime hours OT = 5 Profit P= 3-3*c2^2+42* C2-3*C3^2+46*C

Set up Solver Parameters as follows:

Solver Parameters Х Set Objective: $C$5 1 To: Max Min Value Of: 0 By Changing Variable Cells: $C$2:$C$4 1 Subject to the Cons

Note that this is a nonlinear model, so Select a Solving Method: GRG Nonlinear

Click Solve. After that, values will appear automatically in variable cells (C2:C4)

А B C D E F G H - ㄴ 1 2 Units of product 1 x1 = 3.666666 3 Units of product 2 x2 = 2.666664 4 Overtime hours OT = 6.666649 5

Click OK

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Result:

Units of product 1 x1 = 3.667
Units of product 2 x2 = 2.667
Overtime hours OT = 6.667
Profit P = $ 881.667
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