TRUCKING
Response to the following problem:
Bay City Movers is a local company that specializes in intercity moves. In the business plan submitted to its backers, Bay City has committed itself to a total trucking capacity of at least 42 tons. The company is in the process of replacing its entire fleet of trucks with 1 -ton pickup trucks and 2 j-ton moving van-type trucks. The 1-ton pickup trucks will be manned by one worker, whereas the large vans will utilize a total of four workers for larger moves. Bay City Movers currently employs 63 workers and has facilities for at most 50 trucks. Pickup trucks cost the company $24,000 each; the moving vans cost $60,000 each. The company wishes to make a minimum investment of capital that will provide a trucking capacity of at least 42 tons while not requiring any additional workers or trucking facilities.
a. Use a linear programming model to determine the optimal number of pickup trucks and moving vans Bay City Movers should purchase.
b. There are alternate optimal solutions to this model. Determine the one that:
i. Purchases only one type of truck
ii. Purchases the same number of pickup trucks as moving vans
iii. Purchases the minimum number of trucks