# MATHEMATICS

**Question 1**

Management science techniques focus primarily on observation, model construction and implementation to find an appropriate solution to a problem.

**Question 2**

In linear programming problems, multiple optimal solutions occur when constraints are parallel to each other.

**Question 3**

A change in the value of an objective function coefficient will always change the value of the optimal solution.

**Question 4**

Fractional relationships between variables are not permitted in the standard form of a linear program.

**Question 5**

In a total integer model, all decision variables have integer solution values.

**Question 6**

In a transshipment problem, items may be transported from destination to destination and from source to source.

**Question 7**

The events in an experiment are mutually exclusive if only one can occur at a time.

**Question 8**

The minimax criterion minimizes the maximum payoff.

**Question 9**

Excel can be used to simulate systems that can be represented by both discrete and continuous random variables.

**Question 10**

Adjusted exponential smoothing is an exponential smoothing forecast adjusted for seasonality.

**Question 11**

Which of the following is an equation or an inequality that expresses a resource restriction in a mathematical model?

**Question 12**

If the price decreases but fixed and variable costs do not change, the break even point:

**Question 13**

A slack variable:

**Question 14**

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?

**Question 15**

The following is an Excel “Answer” and “Sensitivity” reports of a linear programming problem:

**The Answer Report:**

**The Sensitivity Report: **

Which additional resources would you recommend to be increased?

**Question 16**

Given the following linear programming problem that minimizes cost.

Min Z = 2x + 8y

Subject to 8x + 4y ≥ 64

2x + 4y ≥ 32

y ≥ 2

What is the sensitivity range for the third constraint, y ≥ 2?

**Question 17**

Compared to blending and product mix problems, transportation problems are unique because:

**Question 18**

The owner of Black Angus Ranch is trying to determine the correct mix of two types of beef feed, A and B which cost 50 cents and 75 cents per pound, respectively. Five essential ingredients are contained in the feed, shown in the table below. The table also shows the minimum daily requirements of each ingredient.

Ingredient

Percent per pound in Feed A

Percent per pound in Feed B

Minimum daily requirement (pounds)

1

20

24

30

2

30

10

50

3

0

30

20

4

24

15

60

5

10

20

40

The constraint for ingredient 3 is: