A large hospital is soliciting competitive bids to contractors for the construction of a new wing. The hospital's procurement auction will use a first-price sealed-bid mechanism. Your construction company plans to bid for this business. You have data on the historical bid frequencies of the average bidder for construction jobs in this area. These data indicate that, for an average bidder, the proportion of relative bids that exceed a relative bid of 1.05 equals 0.84, and the proportion of relative bids that exceed a relative bid of 1.10 equals 0.70. However, for one particular competitor - Rockford Construction - you estimate its likelihood of exceeding a relative bid of 1.05 equals 0.65 and its likelihood of exceeding a relative bid of 1.10 equals 0.50. (a) Briefly describe the concept of expected value. Then, consider this situation: if the roll of a single die shows a 4, you will win $30, but if it shows any other number, you will win nothing. Given this situation, what is the maximum amount one should pay for a roll of the die? (Assume a roll of this die would show each of the numbers between 1 and 6 with equal likelihood.) (b) In the procurement auction, you expect to be bidding against two average bidders and Rockford Construction. Calculate the probability of your company winning the job with the relative bid of 1.05 and the probability of your company winning the job with the relative bid of 1.10. Show your work. (c) If your company's costs to build the new hospital wing would be $800,000, how much profit would your company make from winning the job with a relative bid of 1.05? How much profit would it make from winning the job with a relative bid of 1.10? (d) Given your answers to Parts (b) and (c), calculate the expected profit for your company of the relative bid of 1.05 and of the relative bid of 1.10. Show your work. Based on these calculations, which of these two relative bids should your company bid?