Cloth Corp. manufactures and sells 15 different types of fabrics with varying quality (ranging from F01 to F15). In order to designate the quality of a fabric, each fabric type is assigned a quality score on a scale between 0 and 100. The production planning department of Cloth Corp. is currently in the process of forming the aggregate production plan for year 2018. The data for this plan is specified in below table. fabric type (i) 91 di Vi fabric type (i) 91 d Vi F01 98 200 68 F09 70 900 40 F02 95 500 63 F10 63 2000 39 F03 91 800 61 F11 52 800 38 F04 86 1900 51 F12 48 900 36 F05 80 300 49 F13 45 700 34 F06 77 300 47 F14 41 1200 31 (a) Formulate an integer programming (IP) model for this problem. As a hint, you should first define the following decision variable: xij = { F07 74 1000 45 F15 35 850 30 In the table, q; indicates the quality score of the fabric of type i. d; denotes the demand for fabric of type i in meter squares with a variable production cost of v TL per meter-square. In addition, a fixed cost of f = 50,000 TL is incurred for setting up the factory for the production of any type of fabric. The objective of the planning department is to minimize the total cost of production in 2018 so that all demands are satisfied. F08 73 1300 41 In order to avoid incurring the additional fixed cost of production, Cloth Corp. may choose to fully satisfy the demand for a particular fabric from the production of a fabric of higher quality. For example, the demand for fabric type F09 (with quality score of 70) can be fully satisfied with the production of fabric type F05 (with quality score of 80). Note that there is no partial substitution; that is, 100% of the demand of fabric must be fulfilled either directly from the production of fabric or from the production of a fabric of better quality. Clearly, it is not permissible to substitute a lower quality fabric for a higher quality one. if fabric of type i is used to satisfy the demand of fabric of type j otherwise Obviously, you may need to define additional variables, but you must employ these variables in your formulation. Clearly state all additional variables you define. Provide a short description for each constraint and the objective function. (b) Implement and solve your model in OpenSolver. Report the optimal solution and the optimal objective function value. Interpret your solution. (Which fabric type is used to satisfy the demand of each fabric type?). Comment on any additional observations you may have.