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MSBA7003 Quantitative Analysis Methods

Assignment 3 (Due October 22 at 09:00 a.m.; Please submit your solutions with the

template)

Q1.

Consider the following linear programming problem. Which of the following statement(s)

is(are) true?

A) The corner points of the feasible region are (x1,x2) = (0,0), (0,3), (4,0), and (4,2).

B) The optimal solution is (x1,x2) = (4,2).

C) There is a redundant constraint.

D) There are infinitely many optimal solutions.

E) None of the above.

Q2.

A winner of the Texas Lotto has decided to invest partly or entirely his award of $50,000 in

the stock market. Under consideration are stocks for a petrochemical firm and a public

utility. Being discreet, this person decides to minimize the risk of the investment as long as a

total return of 8% (i.e., $4,000) is generated. A risk index on a scale of 1-10 (with 10 being

the most risky) is assigned to each of the two stocks. Cash savings will generate zero return

but will have zero risk. The total risk of the portfolio is found by multiplying the risk of each

stock by the dollars invested in that stock and then summing them up. The following table

provides a summary of the return and risk:

Stock Estimated Return Risk Index

Petrochemical 12% 9

Utility 6% 4

Which of the following statement(s) is(are) true?

A) The optimal solution is to invest $33,333 in the utility stock and $16,667 in the other

stock.

B) If the investor wants to keep at least $10,000 as cash, the optimal solution will not

change.

C) If the risk of the petrochemical stock is reduced to 8, the optimal solution will not change.

D) If the return rate of the utility stock is increased to 7%, the optimal solution will not

change.

E) None of the above.

Q3.

Consider the worker scheduling problem in the lecture notes (Chapter 6, page 7). Suppose

that the post office can force employees to work one day of overtime each week on the day

immediately following this five-day shift. For example, an employee whose regular shift is

Monday to Friday can also be required to work on Saturday. Each employee is paid $100 a

day for each of the first five days worked during the week and $124 for the overtime day (if

any). The goal of the post office is to minimize the cost of meeting its weekly work

requirements. Which of the following statement(s) is(are) true?

A) The minimum total weekly cost is $11,540.

B) In the optimal solution, the post office needs six workers to start working on Monday.

C) In the optimal solution, the post office needs four workers to work overtime on Monday.

D) In the optimal solution, the post office does not need any workers to start working on

Friday.

E) None of the above.

Q4.

The Salem Board of Education wants to evaluate the efficiency of the town’s four

elementary schools. The three outputs of these schools are: (1) average reading score, (2)

average mathematics score, and (3) average self-esteem score. The three inputs to these

schools are: (1) average educational level of mothers (defined by highest grade completed:

12 = high school graduate, 16 = college graduate, and so on), (2) number of parent visits to

school (per child), and (3) teacher-to-student ratio. The relevant information for the four

schools is given in the table below.

School Input 1 Input 2 Input 3 Output 1 Output 1 Output 3

A 14.5 3 0.25 3.5 2.7 3

B 13 2 0.13 3.3 2.5 2.4

C 15.5 4 0.28 3.8 3 3.3

D 16.2 3 0.33 4 3.8 4

Which of the following statement(s) is(are) true?

A) If we assume constant returns to scale, school A is efficient.

B) If we assume constant returns to scale, school D is not effcient.

C) If we assume non-constant returns to scale, school A is efficient.

D) If we assume non-constant returns to scale, school C is efficient.

E) None of the above.