MGT 2251 - Exam 1

The constraints of an LP model define the a. feasible region b. practical region c. maximal region d. opportunity region

a. feasible region

The shadow price of a nonbinding constraint is a. positive b. zero c. negative d. indeterminate

b. zero

What most motivates a business to be concerned with efficient use of their resources? a. Resources are limited and valuable. b. Efficient resource use increases business costs. c. Efficient resources use means more free time. d. Inefficient resource use means hiring more workers.

a. Resources are limited and valuable.

Given an objective function value of 150 and a shadow price for resource 1 of 5, if 10 more units of resource 1 are added (assuming the allowable increase is greater than 10), what is the impact on the objective function value? a. increase of 50 b. increase of unknown amount c. decrease of 50 d. increase of 10

a. increase of 50

Mathematical programming is referred to as a. optimization. b. satisfying. c. approximation. d. simulation.

a. optimization.

A binding less than or equal to (≤) constraint in a maximization problem means a. that all of the resource represented by the constraint is consumed in the solution. b. it is not a constraint that the level curve contacts. c. another constraint is limiting the solution. d. the requirement for the constraint has been exceeded.

a. that all of the resource represented by the constraint is consumed in the solution.

Binding constraints have a. zero slack. b. negative slack. c. positive slack. d. surplus resources.

a. zero slack.

A set of values for the decision variables that satisfy all the constraints and yields the best objective function value is a. feasible solution. b. an optimal solution. c. a corner point solution. d. both (a) and (c).

b. an optimal solution.

Limited resources are modeled in optimization problems as a. an objective function. b. constraints. c. decision variables. d. alternatives.

b. constraints.

A facility produces two products. The labor constraint (in hours) is formulated as: 350x1+300x2 ≤ 10,000. The number 350 means that a. one unit of product 1 contributes $350 to the objective function. b. one unit of product 1 uses 350 hours of labor. c. the problem is unbounded. d. the problem has no objective function.

b. one unit of product 1 uses 350 hours of labor.

The changes (decrease or increase) in the value of the objective function per unit increase in a right-hand side of constraint is the a. sensitivity value b. shadow price c. constraint coefficient d. slack value.

b. shadow price

The allowable increase for a changing cell (decision variable) is a. how many more units to produce to maximize profit. b. the amount by which the objective function coefficient can increase without changing the optimal solution. c. how much to charge to get the optimal solution. d. the amount by which constraint coefficient can increase without changing the optimal solution.

b. the amount by which the objective function coefficient can increase without changing the optimal solution.

The allowable decrease for a constraint is a. how many more units of resource to purchase to maximize profits. b. the amount by which the resource can decrease given shadow price. c. how much resource to use to get the optimal solution. d. the amount by which constraint coefficient can increase without changing the final optimal value.

b. the amount by which the resource can decrease given shadow price.

The allowable increase for a constraint is a. how many more units of resource to purchase to maximize profits. b. the amount by which the resource can increase given shadow price. c. how much resource to use to get the optimal solution. d. the amount by which the constraint coefficient can increase without changing the final optimal value.

b. the amount by which the resource can increase given shadow price.

The allowable decrease for a changing cell (decision variable) is a. the amount by which the constraint coefficient can decrease without changing final optimal solution. b. an indication of how many more units to produce to maximize profits. c. the amount by which objective function coefficient can decrease without changing the final optimal solution. d. an indication of how much to charge to get the optimal solution.

c. the amount by which objective function coefficient can decrease without changing the final optimal solution.

At the optimal solution for an LP problem, if a constraint has the left-hand-side value does not equal to the right-hand-side values, then which of the following is not true? a. the constraint is nonbinding b. the constraint has positive slack or surplus c. the constraint has zero shadow price d. the constraint has positive shadow price

d. the constraint has positive shadow price

When performing sensitivity analysis, which of the following assumptions must apply? a. All other coefficients remain constant. b. Only right hand side changes really mean anything. c. The X1 variable change is the most important. d. The non-negativity assumption can be relaxed

a. All other coefficients remain constant.

A diet is being developed which must contain at least 100 mg of vitamin C. Two fruits are used in this diet. Bananas contain 30 mg of vitamin C and Apples contain 20 mg of vitamin C. The diet must contain at least 100 mg of vitamin C. Which of the following constraints reflects the relationship between Bananas, Apples and vitamin C? a. 20 A + 30 B ≥ 100 b. 20 A + 30 B ≤ 100 c. 20 A + 30 B = 100 d. 20 A = 100

a. 20 A + 30 B ≥ 100

The following linear programming problem has been written to plan the production of two products. The company wants to maximize its profits. X1 = number of product 1 produced in each batch X2 = number of product 2 produced in each batch MAX: 150 X1 + 250 X2 Subject to: 2 X1 + 5 X2 ≤ 200 3 X1 + 7 X2 ≤ 75175 X1, X2 ≥ 0 How many units of resource one (the first constraint) are used if the company produces 10 units of product 1 and 5 units of product 2? a. 45 b. 15 c. 55 d. 50

a. 45

When a manager considers the effect of changes in an LP model's coefficients he/she is performing a. a random analysis. b. a coefficient analysis. c. a sensitivity analysis. d. a qualitative analysis.

c. a sensitivity analysis.

Linear programming problems have a. linear objective functions, non-linear constraints. b. non-linear objective functions, non-linear constraints. c. non-linear objective functions, linear constraints. d. linear objective functions, linear constraints.

d. linear objective functions, linear constraints.

Level curves are used when solving LP models using the graphical method. To what part of the model do level curves relate? a. constraints b. boundaries c. right hand sides d. objective function

d. objective function