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Case Problem 2: Production Strategy

1. Let BP100 = the number of BodyPlus 100 machines produced
BP200 = the number of BodyPlus 200 machines produced

Max 371BP100 + 461BP200
s.t.
8BP100 + 12BP200 <= 600 Machining and Welding
5BP100 + 10BP200 <= 450 Painting and Finishing
2BP100 + 2BP200 <= 140 Assembly, Test, and Packaging
-0.25BP100 + 0.75BP200 >= 0 BodyPlus 200 Requirement

BP100, BP200 greater than of equal to 0

See attachment for graph

Optimal solution: BP100 = 50, BP200 = 50/3, profit = \$26,233.33. Note: If the optimal solution is rounded to BP100 = 50, BP200 = 16.67, the value of the optimal solution will differ from the value shown. The value we show for the optimal solution is the same as the value that will be obtained if the problem is solved using a linear programming software package such as Excel Solver.

2. In the short run the requirement reduces profits. For instance, if the requirement were reduced to at least 24% of total production, the new optimal solution is BP100 = 1425/28, BP200 = 225/14, with a total profit of \$26,290.18; thus, total profits would increase by \$56.85. Note: If the optimal solution is rounded to BP100 = 50.89, BP200 = 16.07, the value of the optimal solution will differ from the value shown. The value we show for the optimal solution is the same as the value that will be obtained if the problem is solved using a linear programming software package such as Excel Solver.

3. If management really believes that the BodyPlus 200 can help position BFI as one of the leader's in high-end exercise equipment, the constraint requiring that the number of units of the BodyPlus 200 produced be at least 25% of total production should not be changed. Since the optimal solution uses all of the available machining and welding time, management should try to obtain additional hours of this resource.

#### Solution Preview

Case Problem 2: Production Strategy
You can find the excel solution and explanations to formulation in attached excel file: 527080_LP case.xlsx.

1. Let BP100 = the number of BodyPlus 100 machines produced
BP200 = the number of BodyPlus 200 machines produced

We assume that the machines are sold only through authorized dealers and we want to maximize the profit from Authorized dealers
Objective function:
Maximize
\$371 BP100 +\$461 BP200

Subject to :
1. Welding and Machining time constraint:
Time used to manufacture BP100 units of Bodyplus 100 and BP200 units of bodyplus 200 should be less than or equal to time available
8BP100+12BP200<=600

2. Painting and Finishing time constraint:
5BP100+10BP200<=450

3. Assembly, testing and packaging
2BP100+2BP200<=140

4. Minimum number of BP200 machines =25% of total production
BP200>=0.25(BP100+BP200)
or -0.25BP100+0.75BP200>=0

5. Non-negativity Constraint:
BP100, BP200>=0

See Attachment for graphical solution.