Net profit generated by a production facility subject to a number of production constraints

Case studies are used to enable you to apply new concepts, use the tools you have mastered, and improve the 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 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.
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, labour 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 labour — 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 labour 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
• 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.
• 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.