INSTRUCTIONS: INSTRUCTIONS: ANSWER QUESTION ONE (1) AND ANY OTHER TWO QUESTIONS. Please write legible and reason carefully QUESTIONS: 1 A company owns two small factories, A and B. which make the same product. A management decision has to be taken to find the number of hours for which each factory should be operated next week Factory A can operate for a maximum of 75 hours per week. producing 45 kilograms of product an hour Tactory B can operate for a maximum of 50 hours per week. producing 30 kilograms an hour. To meet customer demand, at least 2.700 kilograms must be produced next week. The hourly cost of running Factory A is $2.000 an hour and for Factory B it is $1.000 an hour. Because of State grant regulations, the company must operate Factory A for at least as many hours as Factory B. The company's aim is to minimize running costs. You are required to: a) Write down the objective function and the constraints. 16 marks b) Draw a graph of the problem, shading the leasible region 18 marks c) Identify the redundant constraints and the binding constraints in the above problem, and hence discuss how the binding construint aflects our objective function 16 marks) d) Conduct a sensitivity analysis on the above problem 16 marks e) Recommend a production policy with reasons and comments 14 marks