Suppose we are interested in bidding on a piece of land and we know one other bidder is interested. The seller announced

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Suppose we are interested in bidding on a piece of land and we
know one other bidder is interested. The seller announced that the
highest bid in excess of $25,000 will be accepted. Assume that the
competitor's bid x is a random variable that is uniformly
distributed between $25,000 and $30,000.
(a) Suppose you bid $27,000. What is the probability that your
bid will be accepted?
(b) Suppose you bid $29,000. What is the probability that your
bid will be accepted?
(c) What amount should you bid in dollars to maximize the
probability that you get the property?
(d) Suppose you know someone who is willing to pay you
$31,000 for the property. What is the expected profit in dollars if
you bid the amount given in part (c)? $ Find a bid in dollars which
produces a greater expected profit than bidding the amount given in
part (c). (If an answer does not exist, enter DNE.)
Would you consider bidding less than the amount in part
(c)? Why or why not?
Yes. There is a bid which gives a greater expected profit than
the bid given in part (c), and thus a higher expected profit is
possible with a bid smaller than the amount in part (c). No. The
bid which maximizes the expected profit is the amount given in part
(c), thus it does not make sense to place a smaller bid.