Question

Your company has a customer who is shutting down a production line, and it is your responsibility to dispose of the extrusion machine. The company could keep it in inventory for a possible future product and estimates that the reservation value is $100,000. Your dealings on the secondhand market lead you to believe that if you commit to a price of $200,000, there is a 0.4 chance you will be able to sell the machine. If you commit to a price of $300,000, there is a 0.25 chance you will be able to sell the machine. If you commit to a price of $400,000, there is a 0.1 chance you will be able to sell the machine. These probabilities are summarized in the following table.

For each posted price, enter the expected value of attempting to sell the machine at that price. (Hint: Be sure to take into account the value of the machine to your company in the event that you are not be able to sell the machine.)

Posted Price	Probability of Sale	Expected Value
($)		($)
$400,000	0.1	$
$300,000	0.25	$
$200,000	0.4	$

Assume you must commit to one posted price.

In order to maximize the expected profit of the potential sale, which posted price would you commit to in order to maximize the expected value of the potential sale of the machine?

$200,000

$300,000

$400,000

Answer 1

Answer:
Considering sale price to be $400,000
Expected value = 400,000 * 0.1 + 100,000 * 0.9
= 40,000 + 90,000
= 130,000

Considering sale price to be $300,000
Expected value = 300,000 * 0.25 + 100,000 * 0.75
= 75,000 + 75,000
= 150,000

Considering sale price to be $200,000
Expected value = 200,000 * 0.4 + 100,000 * 0.6
= 80,000 + 60,000
= 140,000

So the potential sale of the machine to maximize the expected value would be at $300,000

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