apu-busn602-problem-set-8

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Part 1 of 5 – Part 1 30.0
Points

The Electrocomp Corporation manufactures two electrical
products: air conditioners and large fans. The assembly process for each is
similar in that both require a certain amount of wiring and drilling. Each air
conditioner takes 3 hours of wiring and 2 hours of drilling. Each fan must go
through 2 hours of wiring and 1 hour of drilling. During the next production
period, 240 hours of wiring time are available and up to 140 hours of drilling
time may be used. Each air conditioner sold yields a profit of $25. Each fan
assembled may be sold for a $15 profit.

Now, Electrocomp’s management also realizes that there
should be a minimum number of air conditioners produced in order to fulfill a
contract. Also, due to an oversupply of fans in the preceding period, a limit
should be placed on the total number of fans produced.

Question 1 of 11 10.0
Points

If Electrocomp decides that at least 20 air conditioners
should be produced but no more than 80 fans should be produced, the optimal
production mix of air conditioners and fans is __________. (The first number is
for air conditioners and the second for fans.)

A.(50,30)

B.(20,80)

C.(40,60)

D.(26.67,80)

Question 2 of 11 10.0
Points

In the optimal solution for the above question (Question 1),
the slack for the four constrains — Total hours of wiring, Total hours of
drilling, Number of air conditioners, Number of fans are __________,
respectively. (Hint: A negative number shows that the constraint is binding
downward, i.e. it sets a lower rather than an upper limit. You may take the
negative sign out when interpreting the results.)

A.0, 0, 20, 20

B.0, 0, 10, 20

C.0, 0, 20, 10

D.10, 10, 10, 10

.

Question 3 of 11 5.0
Points

If Electrocomp decides that at least 30 air conditioners
should be produced but no more than 50 fans should be produced, the optimal
production of air conditioners is 45 and
the optimal production of fans is 50 .
(Please only enter an integer and include no units.)

Question 4 of 11 5.0
Points

In the optimal solution for the above question (Question 3),
the slack for the four constrains — Total hours of wiring, Total hours of
drilling, Number of air conditioners, Number of fans are __________,
respectively. (Hint: A negative number shows that the constraint is binding
downward, i.e. it sets a lower rather than an upper limit. You may take the
negative sign out when interpreting the results.)

A.0, 0, 15, 10

B.5, 0, 15, 0

C.0, 5, 15, 0

D.0, 0, 10, 15

Part 2 of 5 – Part 2 10.0
Points

The Outdoor Furniture Corporation manufactures two products,
benches and picnic tables, for use in yards and parks. The firm has two main
resources: its carpenters (labor force) and a supply of redwood for use in the
furniture. During the next production cycle, 1,200 hours of labor are available
under a union agreement. The firm also has a stock of 3,500 feet of
good-quality redwood. Each bench that Outdoor Furniture produces requires 4
labor hours and 10 feet of redwood; each picnic table takes 6 labor hours and
35 feet of redwood. Completed benches will yield a profit of $9 each, and tables
will result in a profit of $20 each.

Question 5 of 11 10.0
Points

The optimal production of benches is 262 and the optimal production of tables
is 25 . (Please only enter an integer
and include no units. Hint: Because of the resource constraints, you may not be
able to produce 4 tables even if the solution is 3.8; you may have to just
produce 3 tables.)

Part 3 of 5 – Part 3 20.0
Points

A winner of the Texas Lotto has decided to invest $50,000
per year in the stock market. Under consideration are stocks for a
petrochemical firm and a public utility. Although a long-range goal is to get
the highest possible return, some consideration is given to the risk involved
with the stocks. A risk index on a scale of 1–10 (with 10 being the most risky)
is assigned to each of the two stocks. The total risk of the portfolio is found
by multiplying the risk of each stock by the dollars invested in that stock.
The attached table provides a summary of the return and risk. The investor
would like to maximize the return on the investment, but the average risk index
of the investment should not be higher than 6.

Attachments

Question 6 of 11 10.0
Points

The optimal dollar amount invested in Petrochemical stock is
_________ dollars, and the optimal dollar amount invested in Utility stock is
___________ dollars. (Please only enter an integer and include no units. Hint:
The total risk on each stock is the risk index times the investment in dollars.
When you use Excel QM, you need to end thetotal risk in the right hand side of
the constraint not simply the risk index.)

A.20,000, 30,000

B.30,000, 20,000

C.10,000, 15,000

D.15,000, 10,000

Question 7 of 11 10.0
Points

The average risk index (not in dollar amount) for the
optimal investment is 6 , and the
estimated best/maximum return for this investment is 4200 . (Please only enter an integer and
include no units.)

Part 4 of 5 – Part 4 10.0
Points

This part of the question is based on the following
information.

The Heinlein and Krampf Brokerage firm has just been
instructed by one of its clients to invest $250,000 of her money obtained
recently through the sale of land holdings in Ohio. The client has a good deal
of trust in the investment house, but she also has her own ideas about the
distribution of the funds being invested. In particular, she requests that the
firm select whatever stocks and bonds they believe are well rated, but within
the following guidelines:

(a) Municipal bonds should constitute at least 20% of the
investment.

(b) At least 40% of the funds should be placed in a
combination of electronic firms, aerospace firms, and drug manufacturers.

(c) No more than 50% of the amount invested in municipal
bonds should be placed in a high-risk, high-yield nursing home stock.

Subject to these restraints, the client’s goal is to
maximize projected return on investments. The analysts at Heinlein and Krampf,
aware of these guidelines, prepare the attached list of high-quality stocks and
bonds and their corresponding rates of return.

Hint: You will need to rearrange one of the constraints in
this problem so that all variables will be at the left hand side of the
constraint and the right hand side of the constraint will be zero. You may
adjust he sign of the constraint accordingly. For example, rearranging x < y
+ 2 to x – y < 2.

Attachments

Question 8 of 11 10.0
Points

The optimal money invested in the five stocks and bonds —
Municipal bonds, Electronics, Aerospace, Drugs, and Nursing homes are
__________ dollars, respectively.

A.50,000, 50,000, 50,000, 50,000, 50,000

B.50,000, 0, 0, 175,000, 25,000

C.25,000, 0, 0, 175,000, 50,000

D.50,000, 25,000, 25,000, 125,000, 25,000

Part 5 of 5 – Part 5 30.0
Points

Mt. Sinai Hospital in New Orleans is a large, private,
600-bed facility, complete with laboratories, operating rooms, and x-ray
equipment. In seeking to increase revenues, Mt. Sinai’s administration has
decided to make a 90-bed addition on a portion of adjacent land currently used
for staff parking. The administrators feel that the labs, operating rooms, and
x-ray department are not being fully utilized at present and do not need to be
expanded to handle additional patients. The addition of 90 beds, however,
involves deciding how many beds should be allocated to the medical staff for
medical patients and how many to the surgical staff for surgical patients.

The hospital’s accounting and medical records departments
have provided the following pertinent information. The average hospital stay
for a medical patient is 8 days, and the average medical patient generates
$2,280 in revenues. The average surgical patient is in the hospital 5 days and
receives a $1,515 bill. The laboratory is capable of handling 15,000 tests per
year more than it was handling. The average medical patient requires 3.1 lab
tests and the average surgical patient takes 2.6 lab tests. Furthermore, the
average medical patient uses one x-ray, whereas the average surgical patient
requires two x-rays. If the hospital was expanded by 90 beds, the x-ray
department could handle up to 7,000 x-rays without significant additional cost.
Finally, the administration estimates that up to 2,800 additional operations
could be performed in existing operating room facilities. Medical patients, of
course, do not require surgery, whereas each surgical patient generally has one
surgery performed.

Assume that the hospital is open 365 days a year. Round off
your answers to the nearest integer.

Question 9 of 11 10.0
Points

The optimal number of medical patients per year is 265 , and optimal number of surgical patients
per year is 301 . The maximum annual
profit is 50752 dollars. (Please round
to the closest integer and include no units.)

 

Question 10 of 11 10.0
Points

Among the 90 additional beds, _______ beds should be used
for medical patients and _______ beds used for surgical patients.

A.45, 45

B.60, 30

C.61, 29

D.29, 61

Question 11 of 11 10.0
Points

At the optimal, there are
0 empty beds, 876 lab tests of
unused capacity, 65.45 x-rays of unused
capacity, and 695 unused operation rooms
available. (Please round to the closest integer and include no units.)

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