Question 8 (20 points): Reyansh is the production manager for the Jupiter Corporation, which produces 6 types of office desks. These office desks are made of 5 different smaller items as listed in the following Table. The first row of the above Table shows that office desk type 1 is made 9 units of item 1, 5 units of item 2,7 units of item 3, 10 units of item 4 , and 5 units of item 5. The other rows of the Table can be interpreted similarly. The price of buying each units of items 1 to 5 from suppliers are $35,$40,$20,$19, and $45 respectively. The production of each office desk also requires processing on each of 10 machines, with the following processing times (in hours): Each machine is available 65 hours per month. Each office desk manufactured will be sold at the following prices: Tnh0= Reyansh wants to determine the combination of office desks to produce in order to maximize total profit. Part a) Formulate a mathematical programming model for this problem. (5 points) 7/8 Part b) How would you modify the model to ensure that at least 4 types of office desk are produced? ( 3 points) Part c) How would you modify the model to ensure that if office desk 3 or 5 are produced then office desk 1 cannot be produced? ( 3 points) Part d) How would you modify the model to ensure that if office desk 4 is produced then office desk 1 or 3 must be produced? (3 points) Part e) How would you modify the model to ensure that if office desk 3 is produced then office desks 1 and 4 must be produced? ( 3 points) Part f) How would you modify the model to ensure that if office desks 2 and 4 are produced then office desk 5 cannot be produced? ( 3 points) Question 8 (20 points): Reyansh is the production manager for the Jupiter Corporation, which produces 6 types of office desks. These office desks are made of 5 different smaller items as listed in the following Table. The first row of the above Table shows that office desk type 1 is made 9 units of item 1, 5 units of item 2,7 units of item 3, 10 units of item 4 , and 5 units of item 5. The other rows of the Table can be interpreted similarly. The price of buying each units of items 1 to 5 from suppliers are $35,$40,$20,$19, and $45 respectively. The production of each office desk also requires processing on each of 10 machines, with the following processing times (in hours): Each machine is available 65 hours per month. Each office desk manufactured will be sold at the following prices: Tnh0= Reyansh wants to determine the combination of office desks to produce in order to maximize total profit. Part a) Formulate a mathematical programming model for this problem. (5 points) 7/8 Part b) How would you modify the model to ensure that at least 4 types of office desk are produced? ( 3 points) Part c) How would you modify the model to ensure that if office desk 3 or 5 are produced then office desk 1 cannot be produced? ( 3 points) Part d) How would you modify the model to ensure that if office desk 4 is produced then office desk 1 or 3 must be produced? (3 points) Part e) How would you modify the model to ensure that if office desk 3 is produced then office desks 1 and 4 must be produced? ( 3 points) Part f) How would you modify the model to ensure that if office desks 2 and 4 are produced then office desk 5 cannot be produced? ( 3 points)
