Question 6. (19 points) PRODUCTION PROBLEM You work as an operations consultant for a textile company which produces fabrics for 16 different apparel types. Your client has a well-established production system. The fabrics for apparel can be produced in 3 different factories. Each factory's productivity is different and hence the fabric for the same apparel may require different labor hours in each factory. You will work with your client to determine the best way to produce a given type of fabric to maximize the total profits while meeting the demand. The following information will guide you in analyzing the decisions. . . The company has 16 different fabric types to sell. See names in the Excel file. The company has 3 factories in: Brazil, Indonesia, and Spain. For each factory, information on o estimated monthly capacity (in terms of labor hours per shift), and the labor minutes required for each yard of fabric in each factory are provided in the Excel file. Profit per each yard of fabric as well as the monthly demand of each fabric is given in Excel. Each factory works 3 shifts a day and 21 26 days a month. The total production cannot be larger than the demand. O . You will analyze the information provided, build spreadsheet models, and use optimization to make a recommendation to your client on the amount of each type of apparel each factory produces. 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