A computer company is trying to determine how many 2017 versions should be order

Question

A computer company is trying to determine how many 2017 versions should be ordered. Each computer costs $10,000. Each computer is sold for $15,000. The demand for their 2016 computers has the probability distribution listed below. If the demand for 2017 computer falls short, the company may dispose of excess computers in an end-of-model-year sale for $9,000 per computer. How many 2017 computers - should the company order? Number of Computers Demanded - Probability 25 .15 30 .15 35 .25 40 .15 How many should 2017 computers the company order?

Explanation / Answer

As no other criteria is satisfied, we'll consier tha the number of computers is such that the expected value of profit is greater than zero.

Let P be the random variable denoting the profit.

now profit on each sold computer = $15000-$10000 = $5000,

and for unsold computer, profit = $9000-$10000 = -$1000

let the number of computers to be ordered be x

therefore expected profit = sum over the given number computers demanded (pi * xi)*($5000*xi + (-$1000)*max((x-xi), 0) ...(1)

Now, the probability distribution of number of computers given is incomplete, as the probability doesn't add up to 1. Once we have the complete Probability distribution, we can find x in equation (1), by evaluating equation (1) > 0

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