(20 points) Consider a company that produces and sells dairy products in both the U.S and Canada. A U.S shipper charges US$ 0.25 per kg to ship between the two countries. Suppose that the exchange rate is US$1.00 = C$1.30. Assume no taxes and consider the following details:

Professionalism Guidelines (5 points)

Circle your final answers for each question.

Show your work for each question clearly (refer past solution manuals for guidance).

Provide sketches/diagrams/charts wherever requested or you feel is appropriate.

Annual Demand (kg) Annual Capacity (kg) Sales Price (per kg) Production Cost (per kg)

U.S.

24,000

40,000 US$ 3.50 US$ 1.80

Canada

15,000 19,000

5.75 3.90

Currently the Canadian government sets a limit on dairy product imports at 3,000 kg per year as a measure of supply management. It also imposes price controls on dairy products.

What is the best production and distribution plan? (i.e. Calculate how much should be made in each country, and how much should be shipped between the two countries)

Given your plan in part (a), what would be the annual profit in Canada (expressed in C$)?

A new trade agreement signed between the U.S and Canada has made the following key changes relevant to this company:

C$ C$

c.

The Canadian governments import limitation on dairy products has been revised to 20,000 kg per year.

The price control measures have now been eliminated. This lets U.S companies sell imported dairy products at their sales price in the U.S.

Given these developments, what is the best new production and distribution plan?

(i.e. Calculate how much should be made in each country, and how much should be shipped between the two countries)

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Given your plan in part (c), what would be the annual profit in Canada (expressed in C$)?

Considering your answers to parts (b) and (d) above, what do you think is the impact of the new trade agreement between the two countries on the company. Is there a major practical implication that we are not considering in the part (c) calculation?

(10 points) Consider a process with an upper spec limit of 14.5 lbs, a lower spec limit of 10.5 lbs, and a mean of 12 lbs.

If the standard deviation is 0.25 lbs, is the process capable?

If the standard deviation is 0.75 lbs, is the process capable?

Briefly explain, what a process being capable implies.

(15 points) Consider a normally distributed process that cuts wood with a process center of 16 inches and a standard deviation of 0.75 inches. The lower specification limit is 14.75 inches, and the upper specification limit is 17.15 inches. A piece of wood that is cut too short must be scrapped at a cost of $32.00. A piece of wood that is cut too long must be re-cut by hand at a cost of $8.50. The firm runs 20,000 pieces of wood through the machine per day and works 350 days per year.

4.

What is the annual expected fixing cost of this process?