Question 1 Fork Motor Company is an automobile manufacturer operating in the US. It has divided…

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