## (Solved) (10 points) Consider a firm with a plant in the U. and the U.-based shipper charges 0.50 per unit to ship between the two countries. Assume no...

1.Â Â Â Â  (10 points)

Consider a firm with a plant in the U.S. and the U.K. Â A U.K.-based shipper charges â‚¤0.50 per unit to ship between the two countries.Â  Assume no taxes, and consider the following data.

Â Â  U.S.Â Â  Â Â Â Â Â Â Â Â Â Â  Â Â Â U.K.Â Â

Weekly DemandÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  Â Â  13,000Â Â Â Â Â Â Â Â Â  Â Â  24,000

Weekly CapacityÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  Â Â  18,000Â Â Â Â Â Â Â Â Â  Â Â  32,000

Sales PriceÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  Â Â Â Â  \$30Â Â Â Â Â Â Â Â Â Â Â Â  Â Â Â Â Â  â‚¤25

Production CostÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  Â Â Â  Â Â Â \$7Â Â Â Â Â Â Â Â Â Â Â Â  Â Â Â Â Â  Â Â â‚¤5

a.Â  Suppose that the exchange rate is â‚¤1.00 = \$1.60.Â  What is the best production and distribution plan, i.e., how much should be made in each country, and how much should be shipped between countries?

b.Â  Given your plan in part a, what is the profit in each country (expressed in dollars)?

2.Â Â Â Â  (5 points)

Consider a process with an upper spec limit of 69.5 grams, a lower spec limit of 62 grams, and a mean of 67 grams.

a.Â  If the standard deviation is 1 gram, is the process â€œcapable?â€

b.Â  If the standard deviation is 2 grams, is the process â€œcapable?â€

3.Â Â Â Â  (10 points)

Consider a normally distributed process that cuts wood with a â€œprocess centerâ€ of 18 inches and a standard deviation of .08 inches.Â  The lower specification limit is 17.75 inches, and the upper specification limit is 18.18 inches.Â  A piece of wood that is cut too short must be scrapped at a cost of \$22.00.Â  A piece of wood that is cut too long must be re-cut by hand at a cost of \$4.50.Â  The firm runs 20,000 pieces of wood through the machine per day and works 350 days per year.Â  What is the annual expected fixing cost of this process?

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