A Businessman Is Considering Opening a Small Specialized Trucking Firm

Essay

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. $$\begin{array} { c c c c } \text { Truck } & \text { Cost } & \begin{array} { c } \text { Capacity } \\( \text { Cu. Ft.) }\end{array} & \begin{array} { c } \text { Drivers } \\\text { Needed }\end{array} \\\hline \text { Small } & \$ 18,000 & 2,400 & 1 \\\text { Large } & \$ 45,000 & 6,000 & 3\end{array}$$ 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?