VANPOOLING. Logitech, a rapidly growing high-tech company located in suburban Boston, Massachusetts, has been encouraging its employees to carpool. These efforts have met with only moderate success, and now the company is setting aside up to $250,000 to purchase small- and medium-size vans and minibuses to establish a van-pool program that will transport employees between various pickup points and company headquarters. Four models of vans and two models of minibuses are under consideration, as detailed in the following table.
a. Formulate and solve a vehicle purchase model for Logitech that will maximize the total passenger capacity of the fleet given that:
• Up to $250,000 will be spent on vehicles.
• Annual maintenance cost should not exceed $50,000.
• Total number of vehicles purchased should not exceed eight.
• At least one minibus should be purchased.
• At least three vans should be purchased.
• At least half the vehicles should be made in the United States.
b. Determine the optimal solution if the amount Logitech committed for vehicle purchase were: (i) $253,900; (ii) $254,000; (iii) $249,900; (iv) $259,900; (v) $260,000. Comment.
c. Characterize the problem if the amount Logitech committed to the program were $1 0 0 ,0 0 0 .