An automobile manufacturer produces several kinds of vehicles; e.g., cars, trucks, SUV's, etc. Each kind requires a certain amount of factory time per vehicle to produce, and yields a certain profit per vehicle. A certain amount of factory time has been scheduled for the next week, and it is desired to use all this time; but at least a certain number of each kind of vehicle must be manufactured to meet dealer requirements. a) Using the information above, consider how you would define the SETS, members, data, and decision variable(s) for this problem. b) State the objective function in words. Then express that statement mathematically c) State the constraint equation(s) in words. Then express that statement(s) mathematically. d) Now suppose that there are 168 hours of factory time available, and that the time per vehicle, profit per vehicle and dealer orders for each kind of vehicle are as follows: time Vehicle Trucks Cars SUV profit orders 20010 500 20 700 15 An automobile manufacturer produces several kinds of vehicles; e.g., cars, trucks, SUV's, etc. Each kind requires a certain amount of factory time per vehicle to produce, and yields a certain profit per vehicle. A certain amount of factory time has been scheduled for the next week, and it is desired to use all this time; but at least a certain number of each kind of vehicle must be manufactured to meet dealer requirements. a) Using the information above, consider how you would define the SETS, members, data, and decision variable(s) for this problem. b) State the objective function in words. Then express that statement mathematically c) State the constraint equation(s) in words. Then express that statement(s) mathematically. d) Now suppose that there are 168 hours of factory time available, and that the time per vehicle, profit per vehicle and dealer orders for each kind of vehicle are as follows: time Vehicle Trucks Cars SUV profit orders 20010 500 20 700 15