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 $$153,000.$ The current property owner has asked for bids and stated that the property will be sold for the highest bid in excess of $$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 $$100,000$ and $$143,000.$

$($a$)$What is the estimate of the probability Strassel will be able to obtain the property using a bid of $$123,000?($Use at least $5,000$ trials. Round your answer three decimal places.$)$

$($b$)$How much does Strassel need to bid to be assured of obtaining the property?

$$123,000$

$$133,000$

$$143,000$

$($c$)$Use the simulation model to compute the profit for each trial of the simulation run $($noting that Strassel's profit is $$0$ if he does not win the bid$).$ With maximization of profit as Strassel's objective, use simulation to evaluate Strassel's bid alternatives of $$123,000,$ $$133,000,$ or $$143,000.$ 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 $$123,000$ $

expected profit for a bid of $$133,000$ $

expected profit for a bid of $$143,000$ $

What is the recommended bid?

$$123,000$

$$133,000$

$$143,000$