Question

Question 1

Fork Motor Company is an automobile manufacturer operating in the US.

It has divided its market into three regions and has built three regional distribution centers (RDC) to serve these markets. The RDCs are located in California, Florida and Texas.

The annual demand at each regional distribution center is estimated as follows and the company wants to meet all the demand.

- RDC – California: 1.5M automobiles (i.e., 1.5 million)

- RDC – Florida: 0.5M automobiles

- RDC – Texas: 1M automobiles

Fork Motor has two plants in Michigan and Nevada and wants to distribute the automobiles to the RDCs at the lowest cost. So they need to decide how many cars to ship from each of the plants to each of the RDCs to achieve minimum cost. You are asked to model and solve this allocation problem.

Below, you are given the shipping distance between Fork Motor’s facilities in miles.

	Plant – Michigan	Plant – Nevada
RDC – California	2000	300
RDC – Florida	1000	1300
RDC – Texas	1200	800

The head of supply chain informs you that you need to consider the capacity limits of the plants. The Michigan plant is much larger than the one in Nevada. He adds that the capacity limits are as follows:

- Plant – Michigan: 2.5M

- Plant – Nevada: 0.7M

The company estimates that transportation of each car will cost 5.99 dollars per mile.

What is the minimum cost of shipping cars to RDCs in million dollars?

(Round your answer to the nearest integer Million dollar. Do not include the dollar sign or the Million sign. For example, if your answer is 205.8 Million dollars, enter 206.)

Question 2

Management is not satisfied with the cost of distribution and asks you to think of ways to reduce it. One alternative is to build a plant close to Florida RDC to reduce shipping costs. You have found an ideal location in South Carolina. Below are the distances from this new plant to each of the RDCs. The capacity of this plant is 0.5M.

	Plant – South Carolina
RDC – California	1500
RDC – Florida	200
RDC – Texas	700

What would be the minimum transportation cost in million dollars if this plant is built? (Round your answer to the nearest integer million dollar. Do not include the dollar sign or the Million sign. For example, if your answer is 205.8 Million dollars, enter 206.)

Question 3

Once you develop this plan, management informs you that there has been an unexpected storm that has impacted the shipping route between California and Nevada. Therefore, no cars can be shipped between these two states. Fortunately, all other routes are still open. Solve the problem again with this information.

What would be the minimum shipping cost in this case?

Question 4

Now that you have obtained the optimal transportation plan, you want to study production cost. You notice that the cost of producing an automobile as a function of number of products made is convex. You also see that some plants are producing less than their optimal level.

- Which of the following are true for those plants that are produce below optimum level?

Select ALL correct answers

1) If these plants make more products, the total cost of production at those plants will always be lower.

2) If these plants make less products, the cost of production per automobile will be higher.

3) If these plants make less products, the cost of production per automobile will be lower.

4) At the optimal production level, the first derivative of the cost function is zero.

5) At the optimal production level, the second derivative of the cost function is equal to zero.

6) None of the above

Answer 1