NOTE: SHOW ALL YOUR WORK.

For this problem, you will formulate a profit maximization problem and determine the monthly production plan that maximizes the total profits. Your client is not familiar with optimization models. You must clearly explain your approach to computing the maximum profit. To do so,

a) (3 points) Clearly define your decision variables in English. How many decision variables do you have?

NOTE: In your Solver model, the unit of production should be yards of fabric.

b) (2 points) What is the objective function in this problem? Explain how you would compute the objective function (in English). The mathematical expression for the objective function is very long, so do NOT explicitly state the mathematical formula.

c) (4 points) Clearly explain the constraints (in English). What type of constraints do you have? Do NOT provide the mathematical formula for the constraints.

d) (2 point) What are the sign and type restrictions in optimization problems? Are there any sign or type restrictions in this problem? Clearly explain why or why not.

e) Prepare a spreadsheet to determine the optimal production plan using Excel Solver.

i. (2 points) 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.

ii. (2 points) 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.

iii. (2 points) 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.

NOTE: Ignore all type restrictions in this problem. Do not enforce your decision variables to be integerwhile using Excel Solver. If you formulate the problem correctly, the optimal solution provided by the Solver will be in whole numbers even without the type restrictions.

iv. (2 points) Finally, solve the optimization problem using the Simplex LP method in Excel Solver. What is the optimal solution, i.e., the optimal objective function value and the optimal values of decision variables?

NOTE: Do not forget to change the options in the Solver. Unclick ignore integer constraints and set the integer optimality (%) to 0.00001. Use Simplex LP as your solving method.