Question2. A company receives an order for specially designed product. The cost

Question

Question2. 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. (Develop your model and show your calculations)

Explanation / Answer

If 5 products are produces, Expected Number of good products = 4.5 which is not optimum as it will lead to payment of 250000

If 6 produced, Expected number of good products = 5.4 . Bad products = 0.6

Expected profit = 5.4* 80000(per good product) - 6*55000 + 0.6*0 =5.4*80000-330000=102000

If 7 produced, Expected good 6.3, Bad =0.7

Profit = 6.3*80000 - 7*55000 = 119000

Hence, 7 products must be produced.

Probability of losing money = P(0 good)+P(1 )+P(2)+P(3)+P(4) = 7C0 * 0.1^7 + 7C1* 0.1^6*0.9^1 +7C2* 0.1^5*0.9^2+7C3* 0.1^4*0.9^3+7C4* 0.1^3*0.9^4=

0.1^7 + 7* 0.1^6*0.9^1 +21* 0.1^5*0.9^2+35* 0.1^4*0.9^3+35* 0.1^3*0.9^4= 0.02569

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