Data for questions 16-18 The Gilroy Air-Conditioning Company is considering the
ID: 3358651 • Letter: D
Question
Data for questions 16-18 The Gilroy Air-Conditioning Company is considering the purchase of a special shipment of portable air conditioners manufactured in Japan. Each unit will cost Gilroy Ss80, and it will be sold for $125. Gilroy does not want to carry surplus air conditioner over until the following year. Thus, all surplus air conditioners will be sold to a wholesaler for $50 per unit. Assume that the air conditioner demand follows a normal probability distribution with -20 and 0-8. o. What is the probability for recommended order quantity. a. 0.57 b. 0.61 c. 0.70 d. 0.60 17. What is the recommend order quantity? a. 21 b. 23 c. 22 d. 24 I8. What is the probability that Gilroy will sell all unit it orders? a. 0.53 b. 0.40 c. 0.46 d. 0.51Explanation / Answer
18.
Suppose we order Q and let F denote the cumulative probability dist.
We want the value of the last item we order to equal the risk it exposes us to.
The value of the last item is ($125-$80)*(1-F(Q)). Note that (1-F(Q)) is the probability demand exceeds Q.
The risk the last item exposes us to is ($80 -$50)*F(Q).
So, we want F(Q) = 45/75 = .6 (Here, 125-80 = 45 and 125-50 =75)
That means we want the likelihood that we stock out to be 0.4
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