The Owner of a Small Construction Firm Is Excavating at Three

Essay

The owner of a small construction firm is excavating at three sites. He wishes to assign his 5 additional trucks in such a way as to minimize his total costs. Each site can use 0 to 3 additional trucks; no site can use more than 3 trucks efficiently. The following site total costs are known. $$\begin{array} { c | r c c } \text { Number } && { \text { Cost of Excavating } } \\\text { of Trucks }& \text { Site 1 }& \text { Site 2 }& \text { Site 3 }\\\hline 0 & \$ 10000 & \$ 15000 & \$ 20000 \\ 1 & 10000 & 14000 & 18000 \\2 & 9200 & 13250 & 17500 \\3 & 8500 & 12750 & 17250\end{array}$$
a.Use dynamic programming to find the assignment of the additional trucks that minimizes total cost.
b.If the owner had only 4 trucks to assign, what would be the optimal assignment and total cost?