Problem 4 (22 points) FJORT manufactures jeeps and trucks. The number of vehicles that can be sold of each for the next 3 months are shown below. Each jeep sells for $38,000 and each truck for $49,000. It costs $30,000 to produce a jeep and $39,000 to produce a truck. Every vehicle in inventory at the end of the month incurs an inventory cost of $150 per jeep and $200 per truck. During each month at most 1,500 vehicles (i.e., jeeps and trucks combined) can be produced. Production line restrictions dictate that during month 1 at least two-thirds of all cars produced must be jeeps. At the beginning of the first month 1,000 jeeps and 100 trucks are available. Please note that backorders are allowed for one month maximum (i.e. trucks produced in month 2 can satisfy the demand of trucks in month 1. Trucks produced in month 3 can satisfy the demand of trucks in month 2 but not the demand of trucks in month 1). Every vehicle incurs a backorder cost of $180 per jeep and $240 per truck. Month Jeep Truck 1 1200 650 2 1400 675 3 1100 80 Formulate algebraically the above multiperiod production planning problem whose objective is to maximize the net profit while meeting the vehicles demand. Define the decision variables, objective function, and constraints. DO NOT SOLVE.