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Jeff Kaufmann’s machine shop sells a variety of machines for job shops. A customer wants to purchase a model XPO2 drilling machine from Jeff’s store. The model XPO2 sells for $180,000, but Jeff is out of XPO2s. The customer says he will wait for Jeff to get a model XPO2 in stock. Jeff knows that there is a wholesale market for XPO2s from which he can purchase an XPO2. Jeff can buy an XPO2 today for $150,000, or he can wait a day and buy an XPO2 (if one is available) tomorrow for $125,000. If at least one XPO2 is still available tomorrow, Jeff can wait until the day after tomorrow and buy an XPO2 (if one is still available) for $110,000. There is a 0.40 probability that there will be no model XPO2s available tomorrow. If there are model XPO2s available tomorrow, there is a 0.70 probability that by the day after tomorrow, there will be no model XPO2s available in the wholesale market. Three days from now, it is certain that no model XPO2s will be available on the wholesale market.a. What is the maximum expected profit if Jeff makes the purchase today?b. What is the maximum expected profit if Jeff makes the purchase tomorrow?c. What is the maximum expected profit if Jeff makes the purchase two days from now?d. What is the maximum expected profit if Jeff makes the purchase three days from now?e. What should Jeff do?

Respuesta :

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Answer:

a) If Jeff purchases today, then he can expect to earn $30,000.

b) If Jeff decides to wait and try to purchase tomorrow, his expected profit is $22,000.

c) If Jeff decides to wait even more and buy the day after tomorrow, then his expected profit is $8,400.

d) Three days form now there will be no XPO2 available, so his profit is $0.

e) Jeff should purchase the XPO2 today and earn $30,000.

Explanation:

selling price $180,000

  • buys today, then profit = $180,000 - $150,000 = $30,000
  • buys tomorrow, then profit = $180,000 - $125,000 = $55,000 x 40% = $22,000
  • if he buys the day after tomorrow, then profit = $180,000 - $110,000 = $70,000 x 40% x 30% = $8,400
  • if he waits 3 days, then his profit is $0 because there are no XPO2s available.

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