Posted on by Judy

(This is industrial engineering; there was no option for it.) A company receives an order for specially designed product. The cost of producing each item is $55,000. The customer agrees to pay $400,000 for five good products, $480,000 for six good products, and $560,000 for seven good products. Other than the five, six or seven good ones, each good item can be recycled from $5,000. All other remaining bad products must be destroyed. The company agrees to pay the customer $250,000 if at least five good products are not produced. Each product is produced independently; the probability of a having good product is 0.9. Determine the number of products to produce, as well as the probability of losing money on the transaction.

Consider the decision alternatives to produce 5,6,7,8,9,10 products.
Calculate probability of states of nature. States of nature are number of good products produced (0,1,2,… 10 good products)
Calculate the expected profit for each alternative.
This is done in spreadsheet model as below:
https://d2vlcm61l7u1fs.cloudfront.net/media%2F5bc%2F5bcc50cf-8f18-486d-a76c-4e00a434d563%2FphpkS4cz7.png
In the above spreadsheet analysis, we see that maximum expected profit is for 7 number of products produced.
Therefore, number of products to produce = 7
When 7 products are produces, loss occurs when less than 5 good products are produced.
Probability of losing money = SUM(B6:F6) = 0.0257 or 2.57 %
 
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