SportsCo manufactures, among other products, baseballs and basketballs. Their per-unit profit for a baseball is $3, and their per-unit profit for a basketball is $15. Both products are made primarily from the same two raw materials: leather and rubber. A baseball requires 1 ounce of leather and 4 ounces of rubber; a basketball requires 6 ounces of leather and 15 ounces of rubber. SportsCo’s current supplier contract provides them with 8,000 ounces of leather per week, and 30,000 ounces of rubber per week.
SportsCo would like to determine the optimal product mix (i.e., the production quantities that maximize profits). You will formulate a linear programming model for this optimization problem.
NOTE: SHOW ALL YOUR WORK.
What are the decision variables? How many decision variables are there? Clearly explain the decision variables in English and provide the mathematical notation used in the algebraic formulation of the decision problem.
What is the objective function? Clearly explain the objective function in English and provide the mathematical formulation.
What are the constraints of the problem? Clearly explain each constraint in English and provide the mathematical formulation.
Are there any sign or type restrictions in your formulation? Why or why not? Clearly explain the sign and type restrictions (if any).
Prepare a spreadsheet to determine the optimal production mix of using Excel Solver.
Provide a screenshot of your spreadsheet model. The screenshot should show all the cells involved in formulating the optimization problem. NOTE: Do not copy and paste your spreadsheet to your answer report as an Excel object. Instead, capture a screenshot in Excel and paste this as an image.
Provide a screenshot of your spreadsheet with the formula view. You can switch from normal view to formula view in Excel by clicking the CTRL and ~ keys on your keyboard simultaneously.
Prepare the Solver model by logging all the information to the Solver Parameters window in Excel. Provide a screenshot of the Solver Parameters window in Excel.
Solve the optimization problem using Excel Solver. What is the optimal solution, i.e. the optimal cost and the optimal values of decision variables?