Airport rent-a-car is a locally operated business in competition with serveral major firms. ARC is planning a new deal for customers who want to rent a car for only one day and return it to the airport. For $24.95, the company will rent a small economy car to a customer, whose only other expense is to fill the car with gas at the day's end. ARC is planning to buy a number of small cars from the manufacturer at a reduced price of $6,750 per car. To simplify things, ARC is considering only three options: buy 10, buy 12 or buy 15 cars.

The big question is how many to buy. Company executives have decided on the following estimated probabilty distribution of the customer demand for rental cars each day: *Customer demand 10 11 12 13 *Probability 0.10 0.40 0.30 0.20 The company antipates that its variable cost per car per day will be $2.25. After using the cars for 1 year, ARC expects to sell them and recapture 45 percent of the original cost. That means 55 percent of the $6,750 cost of each car must be recovered from customers in addition to the variable costs. This works out to an additional cost of $11.90 per day.

1. Prepare a payoff table. Each payoff should represent an amount per day.

2. Determine the optimal number of cars for ARC to buy.

Academic requirements:

• Your work should be submitted in the formats outlined for each queston in the assignment.