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A company manufactures two products. Each product can be produced on either of two machines. Machine A takes 3 hours to produce one product 1 and 4 hours to produce one product 2. Machine B takes 2...

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A company manufactures two products. Each product can be produced on either of two machines.

  • Machine A takes 3 hours to produce one product 1 and 4 hours to produce one product 2. Machine B takes 2 hours to produce one product 1 and 3 hours to produce one product 2. Each month 1000 hours of time are available for production with each machine.
  • Moreover, the production of each product requires a particular number of hours of skilled labor. Producing one product 1 needs 1.5 hours of labor and producing one product 2 needs 2 hours of labor. Each month 1800 hours of skilled labor are available for production.
  • The 1 unit selling price of product 1 is $200 and that of product 2 is $225 for the coming month.
  • The total production quantity of the two products should not exceed 800 units for the coming month.

The company seeks to determine a production plan that maximizes monthly total revenue. An LP formulation of this problem is provided in the Excel file. This formulation is not correct.

Question:

Find all the mistakes in the spreadsheet provided (you should also check the setup of the Solver options). Modify the spreadsheet to setup the model correctly. Alternatively, you can setup the correct model and then compare with the model provided to identify the mistakes.

Answered Same Day May 26, 2022

Solution

Bikash answered on May 27 2022
99 Votes
Answer Report 1
    Microsoft Excel 16.0 Answer Report
    Worksheet: [Production.xlsx]Sheet1
    Report Created: 5/26/2022 9:29:22 PM
    Result: Solver found a solution. All Constraints and optimality conditions are satisfied.
    Solver Engine
        Engine: Simplex LP
        Solution Time: 0.031 Seconds.
        Iterations: 2 Subproblems: 4
    Solver Options
        Max Time Unlimited, Iterations Unlimited, Precision 0.000001, Use Automatic Scaling
        Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 1%, Assume NonNegative
    Objective Cell (Max)
        Cell    Name    Original Value    Final Value
        $C$6    Objective to Maximize Revenue Product 1    0    66625
    Variable...
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