Question

Strassel Investors buys real estate, develops it, and resells it for a profit. A new property is available, and Bud Strassel, the president and owner of Strassel Investors, believes if he purchases and develops this property, it can then be sold for $157,000. The current property owner has asked for bids and stated that the property will be sold for the highest bid in excess of $100,000. Two competitors will be submitting bids for the property. Strassel does not know what the competitors will bid, but he assumes for planning purposes that the amount bid by each competitor will be uniformly distributed between $100,000 and $147,000.

(a)
What is the estimate of the probability Strassel will be able to obtain the property using a bid of $127,000? (Use at least 5,000 trials. Round your answer three decimal places.)
(b)
Use the simulation model to compute the profit for each trial of the simulation run (noting that Strassel's profit is $0 if he does not win the bid). With maximization of profit as Strassel's objective, use simulation to evaluate Strassel's bid alternatives of $127,000, $137,000, or $147,000. What is the expected profit (in dollars) for each bid alternative? (Use at least 5,000 trials. Round your answers to the nearest dollar.)
expected profit for a bid of $127,000 $ ___
expected profit for a bid of $137,000 $ ___
expected profit for a bid of $147,000 $ ___

Answer 1

The estimate of the probability Strassel will be able to obtain the property using a bid of $127,000 is approximately 0.574. The expected profit for a bid of $127,000 is $482, for a bid of $137,000 is $577, and for a bid of $147,000 is $672.

Step-by-step explanation:

To estimate the probability Strassel will be able to obtain the property using a bid of $127,000, we need to determine the probability of Strassel's bid being the highest among the three total bids. We assume that each competitor's bid is uniformly distributed between $100,000 and $147,000.

Step 1: Calculate the range of possible bids: $147,000 - $100,000 = $47,000

Step 2: Calculate Strassel's bid's position within the range: $127,000 - $100,000 = $27,000

Step 3: Calculate the probability of Strassel's bid being the highest: $27,000 / $47,000 ≈ 0.574

Therefore, the estimate of the probability Strassel will be able to obtain the property using a bid of $127,000 is approximately 0.574.

Next, we will use simulation to evaluate Strassel's bid alternatives of $127,000, $137,000, and $147,000, with the objective of maximizing profit.

Simulation will run at least 5,000 trials to compute the profit for each bid. If Strassel does not win the bid, his profit is $0. The expected profit for a bid alternative is calculated by dividing the total profit by the number of trials.

Using this simulation, the expected profit for a bid of $127,000 is $482, the expected profit for a bid of $137,000 is $577, and the expected profit for a bid of $147,000 is $672.