For a new Bond movie which is going to be released soon (i.e., is there ever a t

Question

For a new Bond movie which is going to be released soon (i.e., is there ever a time that a new Bond movie is not about to be released?), a producer of stylish watches has received the exclusive rights to sell a Bond-branded watch. The sales price, as negotiated in the contract, is $350, and these cost the producer $150 to assemble and ship to the stores. Their contract stipulates that 6 months after the Blu-Ray release of the movie, the watches have to be destroyed (since a new Bond movie is then already on the horizon), and are thus worthless. Assume that the producer is facing a one-shot production cycle and that it is impossible to produce additional watches later on. The demand for these watches is normally distributed with a mean of 15,000 and a standard deviation of 2,500. Determine the optimal number of watches to produce. A. 15,450 B. 15,000 C. 17,500 D. 14,550

Explanation / Answer

Co = cost to the producer - resale price. Now the watches are worthless and so the resale price will be nil.

Thus Co = 150 - 0 = 150. Cu = selling price - cost price = 350-150 = 200.

The applicable fractile = Cu/(Cu+Co) = 200/(150+200) = 200/350 = 57.14%

Corresponding z value for 57.14% = 0.18 (from z-score table).

Optimal quantity (Q) = mean+z*standard deviation = 15,000+(0.18*2500) = 15,000+450 = 15,450.

Hence the answer is "A" - 15,450

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