Shocs Shoes Clogging your Feet One Step at a Time Office of the President TO: Productions Manager - MalaysiaFROM: Mark Begich, COOSUBJECT: Limit production

I've just arrived back from meetings with the president of our company in Washington, D.C. As you know the stock price of our parent company has been suffering and the president is under pressure to boost profits. To this end, the company has decided to set internal rate of return targets on all US divisions and on all foreign subsidiaries.

I contacted our sales and logistics divisions on the plane trip back and the latest information I have is as follows:1. The negotiated wholesale distribution price is fixed at $7.54 per pair.2. Based on conversations I have had with our production engineers, they insist that the standard factory design costs are quadratic. (specifically, it follows the form total cost= a + bQ2 functional form)3. The accounting department has analyzed your production costs from an internal audit of the last 8 years and estimated that the cost function is C(Q) = 115.72 + 0.063Q2

I have determined that based on this data, production has been exceeding your monthly quota of 30,000 pairs in most months. Your average cost is also higher than the target $5 per pair established by headquarters. You need to limit your production, as it is too costly.

I want you to implement these production changes in the Malaysia factory immediately, or give a justification of why you should maintain higher production runs.

Parent Company Demands Results!!

Regards, Mark

cc: Lisa Murkowski, Chairman

Response:

Shocs Shoes Clogging your Feet One Step at a Time Office of the President

TO: Mark Begich, COOFROM: Productions Manager - MalaysiaSUBJECT: Re: Expand production

Dear Mark,

Based on the numbers you gave us, our target production should be about 59,800, over a 50% increase over our average production. See below for the workout. I think our biggest concern is avoiding production overruns since we start to lose money on units past this amount. However, the lost sales by under-producing outweigh the alternative of higher costs.My understanding is that the floor managers are just trying to maintain quota, and only exceed it when they try to pass out overtime to the workers. It seems we are leaving money on the table. Now that we have a clear target production, profits should increase 157%.

Sincerely,

Production Team Manager

cc: Lisa Murkowski, Chairman

Solution: When we regressed output on costs using the cubic cost function we find that Q and Q3 are insignificant. Pulling those out, we run the regression of Q2 on total costs to get C(Q) = 115.72 + 0.063Q2. The price is constant for output so Revenue(Q) = 7.54Q. Taking the derivative of each and setting them equal to each other we get C'(Q) = 0.126Q = 7.54 = R'(Q) Q = 59.8. This means that the cost of producing the 59,800th pair of shoes is exactly equal to the revenue we earn from it.The profit from this is R(Q) - C(Q) = 7.54*59.8 - 115.72 - (59.8)2 = $108,900/month

What should the correct price and output be?