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Quantitative Method Multiple Choice Questions

Answer the following multiple choice problems:

1. The minimization of cost or maximization of profit is the
a. objective of a business
b. constraint of operations management
c. goal of management science
d. objective of linear programming
e. both a and d

2. Cully furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. What is the storage space constraint?
a. 90B + 100M 18000
b. 90B + 100M 18000
c. 100B + 90M 18000
d. 500B + 300M 18000
e. 300B + 500M 18000

3. The production manager for the Coory soft drink company is considering the production of 2 kinds of soft drinks: regular and diet. Two of her limited resources are production time (8 hours = 480 minutes per day) and syrup (1 of her ingredients) limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. Which of the following is not a feasible production combination? Please show complete work. Only answer carries no marks.
a. 90R and 75D
b. 135R and 0D
c. 0R and 120D
d. 75R and 90D
e. 40R and 100D

4. Mallory Furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. If the Mallory Furniture company decides to purchase 150 big shelves and no medium shelves, which of the two resources will be left over? Please show complete work. Only answer carries no marks.
a. investment money only
b. storage space only
c. investment money and storage space
d. neither investment money nor storage space

5. Which of the following could not be a linear programming problem constraint?
a. 1A + 2B < 5
b. 1A + 2B 3
c. 1A + 2B = 3
d. 1A + 2B + 3C + 4D 5
e. 1A + 3B 6

6. Given the following linear programming problem:
Min Z = 2x + 8y
Subject to (1) 8x + 4y 64
(2) 2x + 4y 32
(3) y 2
Please show complete work. Only answer carries no marks.
At the optimal solution the minimum cost is:
a. $30
b. $40
c. $50
d. $52
d. $53.33

7. The dietitian for the local hospital is trying to control the calorie intake of the heart surgery patients. Tonight's dinner menu could consist of the following food items: chicken, lasagna, pudding, salad, mashed potatoes and jello. The calories per serving for each of these items are as follows: chicken (600), lasagna (700), pudding (300), salad (200), mashed potatoes with gravy (400) and jello (200). If the maximum calorie intake has to be limited to 1200 calories. What is the dinner menu that would result in the highest calorie in take without going over the total calorie limit of 1200? Please show complete work. Only answer carries no marks.
a. chicken, mashed potatoes and gravy, jello and salad
b. lasagna, mashed potatoes and gravy, and jello
c. chicken, mashed potatoes and gravy, and pudding
d. lasagna, mashed potatoes and gravy, and salad
e. chicken, mashed potatoes and gravy, and salad

8. In a media selection problem, the estimated number of customers reached by a given media would generally be specified in the _________________. Even if these media exposure estimates are correct, using media exposure as a surrogate does not lead to maximization of ______________.
a. problem constraints, sales
b. problem constraints, profits
c. objective function, profits
d. problem output, marginal revenue
e. problem statement, revenue

9. If Xab = the production of product a in period b, then indicate that the limit on production of the company's "3" products in period 2 is 400.
a. X32 400
b. X21 + X22 + X23 400
c. X12 + X22 + X32 400
d. X12 + X22 + X32 400
e. X23 400

10. Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8,000 gallons of component 1 available, and the demand gasoline types 1 and 2 are 11,000 and 14,000 gallons respectively. Write the constraint stating that the component 1 cannot account for more than 35% of the gasoline type 1.
a. x11 + x12 (.35)(x11 + x21)
b. x11 .35 (x11 + x21)
c. x11 .35 (x11 + x12)
d. -.65x11 + .35x21 0
e. .65x11 - .35x21 0

11. Let: rj = regular production quantity for period j, oj =overtime production quantity in period j, ii = inventory quantity in period j, and di = demand quantity in period j
Correct formulation of the demand constraint for a multi-period scheduling problem is:
a. rj + oj + i2 - i1 di
b. rj + oj + i1 - i2 di
c. rj + oj + i1 - i2 di
d. rj - oj - i1 + i2 di
e. rj + oj + i2 - i1 di

12. Which of the following is not an integer linear programming problem?
a. pure integer
b. mixed integer
c. 0-1 integer
d. continuous

13. If we are solving a 0-1 integer programming problem, the constraint x1 x2 is a ________________constraint.
a. multiple choice
b. mutually exclusive
c. conditional
d. co-requisite
e. none of the above

Solution Preview

Please see below for help on the above multiple choice questions. During the copy-paste process, at your end some of the constraint signs (>=, <=, = and not equal to) got deleted. In some questions the signs are not visible in the posted questions. For such questions, refer to your original question. As well, an Excel attachment file is provided for one of the questions - at that question, I have stated to view the attachment file.
Response:

1.
- Answer is 'a': minimization of cost or maximization of profit if not a goal of management science and linear programming. Management science covers variety of tools and techniques other than linear programming. An objective of linear programming can be maximization of revenue or welfare and minimization of time etc.
It is objective of business to minimize cost or maximize profit

2.
- Answer is 'c': Let B and M be the number of big and medium shelves purchased, respectively.
Each big shelf requires 100 cubic feet of storage space and each medium shelf requires 90 cubic feet of storage space. The warehouse has 18000 cubic feet available for storage. Therefore the constraint is 100B + 90M <= 18000.

3.
- Answer is 'd': Let R and D be the quantity of cases (per day) of regular and diet soft drinks manufactured respectively.
To check feasibility ...

$2.19