Wilkinson Auto Dealership Is Contemplating Selling One or More of the Following

Essay

Wilkinson Auto Dealership is contemplating selling one or more of the following types of automobilessedans, SUV's, and trucks. There is a fixed license fee per year for doing business in each line, $\$ 100,000$ , $\$ 250,000$ , and $\$ 50,000$ , respectively. The profit contribution exclusive to the fixed cost is $\$ 250.00$ per unit for sedans, $\$ 700.00$ per unit for SUV's, and $\$ 150.00$ per unit for trucks. The company is planning the placement of orders with the manufacturer for next year. Dealer preparation takes 2 hrs/sedan, 3.0 hrs/SUV, and 1.5 hrs/truck. They have 4400 hrs of preparation time next year. Sedans take 1 unit of space, SUV's take 1.5 units of space, and trucks take 1.1 units of space. 1200 units of space are available. How many sedans, SUV's, and trucks should be ordered in order to maximize total profit contribution less fixed costs incurred? Define the decision variables, constraints, and the objective function for this problem. (Allow the order quantities to be fractional).