a) Formulate the above problem as an appropriate mathematical model. Clearly define all variables, and label each constraint. (15 marks)

b) Solve the problem using EXCEL SOLVER, and recommend the Optimal production plan to the Star-Trucking company. (10 marks)

c) The company has an opportunity to request the United Planets to relax (i.e. remove) one of the two policy restrictions. Which policy do you recommend that the company should request for? What will be the benefit to the company in case United Planets accepts this request? (5 marks)

Q.3 (30 marks) The Product Development team at Star-Trucking Manufacturing Company has developed Space-Hopper in year 2220, a vehicle used for inter-planetary travel. According to its estimates, it needs to provide at least 58,000 Space-Hoppers in the coming year 2221. In order to satisfy this demand, the company is considering the following possible sites for production. The list of these possible sites along with the relevant information is given below: SITE Annual Fixed Cost Variable Cost Annual (in Zens) Per Unit Capacity (in Zens) (in units) Mars 160,000 21 31,000 Jupiter 270,000 33 20,000 Neptune 310,000 29 15,000 Saturn 150,000 31 12,000 Mercury 250,000 18,000 Venus 290,000 39 19,000 27 Based on the regulations of The United Planets, following Policy restrictions are also imposed: Policy-l: No more than three sites may be selected Policy-2: If Mars is selected, then Venus must also be selected Help the company in determining the optimal plan for meeting the demand of Space-Hoppers. Q.3 (30 marks) The Product Development team at Star-Trucking Manufacturing Company has developed Space-Hopper in year 2220, a vehicle used for inter-planetary travel. According to its estimates, it needs to provide at least 58,000 Space-Hoppers in the coming year 2221. In order to satisfy this demand, the company is considering the following possible sites for production. The list of these possible sites along with the relevant information is given below: SITE Annual Fixed Cost Variable Cost Annual (in Zens) Per Unit Capacity (in Zens) (in units) Mars 160,000 21 31,000 Jupiter 270,000 33 20,000 Neptune 310,000 29 15,000 Saturn 150,000 31 12,000 Mercury 250,000 18,000 Venus 290,000 39 19,000 27 Based on the regulations of The United Planets, following Policy restrictions are also imposed: Policy-l: No more than three sites may be selected Policy-2: If Mars is selected, then Venus must also be selected Help the company in determining the optimal plan for meeting the demand of Space-Hoppers