MATHEMATICS

6. The optimal dollar amount invested in Petrochemical stock is 20000 dollars, and the optimal  dollaramount invested in Utility stock is 30000 dollars. (Only use 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 the total 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

7. 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 use an integer and include no units).

 

Part 4 of 5

 

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.

 

Investment

Projected Rate of Return (%)

Los Angeles municipal bonds

5.3

Thompson Electronics, Inc

6.8

United Aerospace Corp.

4.9

Palmer Drugs

8.4

Happy Days Nursing Homes

11.8

 

8. 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

 

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.

 

9. The optimal number of medical patients per year is 2791, and the optimal number of surgical patients per year is 2104. The maximum annual profit is9551040 dollars. (Please round to the closest integer and include no units)

10. 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

11. At the optimal, there are 2 empty beds, 877.5lab tests of unused capacity, 1x-rays of unused capacity, and 696unused operation rooms available. (Please round to the closest integer and include no units.)

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