(Solved): Problem 1 A contractor has a borrow pit from which he may remove sand and gravel and supply to a co ...

Problem 1 A contractor has a borrow pit from which he may remove sand and gravel and supply to a construction site. He is contemplating offering the following bids: Bid A Bid on supplying $400{\mathrm{yd}}^3$ of material. Bid B Bid on supplying $600{\mathrm{yd}}^3$ of material. Bid C Do not bid. The contractor's profit will depend upon the depth of material in the borrow pit $x$. He does not know the exact depth, but estimates his profit $P$ as follows: Bid A $\begin{array}{lll}\text{ Bid A }& P=\$900& \text{ if }9\mathrm{ft}?x?15\mathrm{ft}\\ & P=\$1000& \text{ if }15\mathrm{ft}<x?21\mathrm{ft}\\ \text{ Bid B }& P=?\$200& \text{ if }9\mathrm{ft}?x?15\mathrm{ft}\\ & P=\$2000& \text{ if }15\mathrm{ft}<x?21\mathrm{ft}\end{array}$ Before submitting a bid the contractor is contemplating having a $\$500$ seismic test performed. The seismic test is an imperfect test with a sample likelihood of The contractor is also considering submitting a bid without relying on seismic testing. He has some prior knowledge about the depth, and he estimates that there is an equally likely chance that the actual depth of material in the borrow pit is either between 9 and $15\mathrm{ft}$ or between 15 and $21\mathrm{ft}$. (a) Draw a sequential decision tree for the two test options and three bid options. (b) Prepare a payoff matrix for all possible outcomes. (c) Utilize decision analysis to determine the best test and bid plan. (d) Disregard the answer obtained in part c, and use the decision tree and other information obtained above to determine what the best bid should be if a seismic test is performed and a depth reading of $18\mathrm{ft}$ is obtained.