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# Develop a linear programming model and is solve it using Excel’s Solver tool

Description:

Case studies are used to enable you to apply new concepts, use the tools you have mastered, and improve your technical skills you have attained. Through the individual case studies you will discover for yourself the usefulness of quantitative problem solving methods, how to apply them in practice, and their benefit to organizational decision-makers. In this case study, you will act as a consultant for a manufacturing company looking to maximize net profit generated by a production facility subject to a number of production constraints. You will develop a linear programming model and is solve it using Excel’s Solver tool. Further, you will interpret the generated Answer and Sensitivity Reports to develop recommendations for optimal product mix and future profitability of the company. Both a written report and an Excel spreadsheet model are required to be submitted. Scenario: ABCD, Ltd. is a sports equipment manufacturer that owns and operates a number of manufacturing plants across the country. The company operates one particular plan where both footballs and basketballs are manufactured.

While the company has some flexibility to move manufacturing effort between basketball and football production, the current processes do impose limits on the minimum and maximum number of each ball that can be produced. Production capacity, cost of materials, labor costs, manufacturing time, and other known constraints are provided below: Production Capability and Constraints (All unit costs are in \$ and time in hours): Total Machine hours available: Min 39,000 – Max 40,000 hrs. The number of basketballs that can be produced: Min 30,000 – Max 60,000 The number of footballs that can be produced: Min 20,000 – Max 40,000 Time to manufacture a Basketball: 0.5 hrs. Time to manufacture a Football: 0.3 hrs. Cost of labor -- 1 machine hour: \$6.00 Cost of material-- 1 Basketball: \$2.00 Cost of material-- 1 Football: \$1.25 ABCD believes it can sell each basketball for \$14.00 and each football for \$11.00. Further, the company believes that cost of material and labor costs will not change over the next production cycle.

The corporate tax rate is 28%. The company wants to determine the ideal number of basketballs and footballs to manufacture that will maximize the facility’s net profit after taxes. Management Report: Prepare a written management report that includes, at a minimum, the following sections Purpose of the Report; Description of the Problem; Methodology (which would include the model formulation); Findings or Results; and Recommendations or Conclusions. Be sure to address all relevant points, discuss any assumptions you are making, and highlight the following items in your report: a recommendation for the number of basketballs and footballs to manufacture that maximizes net profit after taxes given the existing constraints; a discussion of which constraints are binding, and the amount of slack or surplus in the remaining constraints; and a list of recommendations as to what actions the company may take in the future to increase profitability, and how much extra profit the company might expect if the action is taken.

Note that these values can be used by the company to determine whether the expected gain in net profit will offset any capital investment required to implement your recommendations. Remember that you are writing the report from the point of view of a consultant with senior management of ABCD, Ltd. as the intended audience. Hints: You need to assume, or guess, an initial number of production units for each product and proceed with using Excel to calculate your Net Revenue for manufacturing. It is ideal to set up a separate section on your spreadsheet that presents the information to be used in the analysis.

This information should be organized under the headings “Changing Cells”, “Constants”, “Calculations”, & “Income Statement”. Once your spreadsheet model is designed, you can proceed with setting Excel SOLVER to carry the calculation. Excel SOLVER is an add-in for MS Excel that can be used for optimization, and other linear programming models. Appendix 7.1 on page of 298 of your textbook provides an overview of how to formulate a model and use Solver to extract the required information. Please also note that your tax will be applied to your Net profit [TR – TC], and if your total cost [TC] is greater than your total revenue [TR], you will have a loss that will be exempted from tax. So, in calculating your Tax you need to use an “IF Statement”, i.e., IF (profit <=0, then put Tax=0, otherwise calculate Tax).