A Businessman Is Considering Opening a Small Specialized Trucking Firm

Short Answer

A businessman is considering opening a small specialized trucking firm. To make the firm profitable, it is estimated that it must have a daily trucking capacity of at least 84,000 cu. ft. Two types of trucks are appropriate for the specialized operation. Their characteristics and costs are summarized in the table below. Note that truck 2 requires 3 drivers for long haul trips. There are 41 potential drivers available and there are facilities for at most 40 trucks. The businessman's objective is to minimize the total cost outlay for trucks. $\begin{array}{cccc}&&\text { Capacity } &\text { Drivers }\\\text { Truck }&\text { Cost }& (\mathrm{Cu} . \mathrm{ft}) & \text { Needed } \\\hline \text { Small } & \$ 18,000 & 2,400 & 1 \\\text { Large } & \$ 45,000 & 6,000 & 3\end{array}$ Solve the problem graphically and note there are alternate optimal solutions. Which optimal solution:
a.uses only one type of truck?
b.utilizes the minimum total number of trucks?
c.uses the same number of small and large trucks?