LPP_MCQ_1

Module B: Linear Programming Multiple Choice

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1 .

When using a graphical solution procedure, the region bounded by the set of constraints is called the [Hint]

solution

feasible region

infeasible region

maximum profit region

2 .

Which of the following is not a property of linear programming problems? [Hint]

the presence of restrictions

optimization of some objective

usage of only linear equations and inequalities

all of the above are properties of linear programming

3 .

A feasible solution to a linear programming problem [Hint]

must satisfy all of the problem's constraints simultaneously

need not satisfy all of the constraints, only some of them

must be a corner point of the feasible region

must give the maximum possible profit

4 .

Consider the following linear programming problem:

Maximize 12X + 10YSubject to: 4X + 3Y = 4802X + 3Y = 360all variables 0

The maximum possible profit for the objective function is [Hint]

1440

1520

1600

1800

5 .



Which of the following points (X,Y) is not feasible? [Hint]

(0,100)

(100,10)

(70,70)

(20,90)

6 .



The feasible corner points are (48,84), (0,120), (0,0), and (90,0). What is the maximum possible value for the objective function? [Hint]

360

1032

1200

1600

7 .

Which of the following is not a property of all LP problems? [Hint]

it seeks to maximize or minimize some quantity

constraints limit the degree to which we can pursue our objectives

there are alternative courses of action to follow

all of the above are properties of LP problems

8 .

Which of the following is not an example of an application of linear programming. [Hint]

scheduling school buses to minimize distance traveled when carrying students

scheduling tellers at banks so service requirements are met during each hour of the day while minimizing the total cost of labor

picking blends of raw materials in feed mills to produce finished feed combinations at minimum cost.

all of the above are examples of LP applications

9 .

Which of the following is a mathematical expression in linear programming that maximizes or minimizes some quantity. [Hint]

objective function

constraints

decision variables

all of the above

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Chapter 10: Linear programming and... Multiple choice questions

Try the following multiple choice questions to test your knowledge of Chapter 10. Once you have answered the questions, click on Submit Answers for Grading to get your results.

A company manufactures two products X and Y. Each product has to be processed in three departments: welding, assembly and painting. Each unit of X spends 2 hours in the welding department, 3 hours in assembly and 1 hour in painting. The corresponding times for a unit of Y are 3, 2 and 1 hours respectively. The employee hours available in a month are 1,500 for the welding department, 1,500 in assembly and 550 in painting. The contribution to profits are 100 for product X and 120 for product Y.

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1 .

What is the objective function (Z) to be maximised in this linear programming problem (where Z is total profit in s)?

Z = 2X + 3Y

Z = 120X + 100Y

Z = 1500X + 1500Y

Z = 100X + 120Y

2 .

Total profits are maximised when the objective function (as a straight line on a graph) is:

Nearest to the origin irrespective of the feasible region

Furthest from the origin and tangent to the feasible region

Nearest to the origin and tangent to the feasible region

Furthest from the origin irrespective of the feasible region

3 .

What is the equation of the labour constraint line for the welding department in this linear programme?

3X + 2Y = 550 hours

3X + 2Y = 1,500 hours

2X + 3Y = 550 hours

2X + 3Y = 1,500 hours

4 .

What is the equation of the labour constraint line for the assembly department in this linear programme?

1X + 1Y = 550 hours

1X + 1Y = 1,500 hours

2X + 2Y = 1,500 hours

3X + 2Y = 1,500 hours

5 .

What is the solution to this linear programming problem in terms of the respective quantities of X and Y to be produced if profits are to be maximised?

X = 150, Y = 400

X = 400, Y = 150

X = 550, Y = 0

X = 0, Y = 500

6 .

Which of the following is NOT an assumption of linear programming?

Prices of products remain the same no matter how high the consumer demand

Constant returns to the variable factors of production

Prices of factor inputs remain the same no matter how high the firm demand

Diminishing returns to the variable factors of production

Which of the following is a property of all linear programming problems?

alternate courses of action to choose from

minimization of some objective

a computer program

usage of graphs in the solution

usage of linear and nonlinear equations and inequalities

A point that satisfies all of a problem's constraints simultaneously is a(n)

maximum profit point.

corner point.

intersection of the profit line and a constraint.

intersection of two or more constraints.

None of the above

The first step in formulating an LP problem is

graph the problem.

perform a sensitivity analysis.

identify the objective and the constraints.

define the decision variables.

understand the managerial problem being faced.

LP theory states that the optimal solution to any problem will lie at

the origin.

a corner point of the feasible region.

the highest point of the feasible region.

the lowest point in the feasible region.

none of the above

In order for a linear programming problem to have a unique solution, the solution must exist

at the intersection of the nonnegativity constraints.

at the intersection of a nonnegativity constraint and a resource constraint.

at the intersection of the objective function and a constraint.

at the intersection of two or more constraints.

none of the above


Maximize

12X + 10Y

Subject to:

4X + 3Y 480

2X + 3Y 360

all variables 0

Which of the following points (X,Y) could be a feasible corner point?

(40,48)

(120,0)

(180,120)

(30,36)

none of the above


Maximize

12X + 10Y

Subject to:

4X + 3Y 480

2X + 3Y 360

all variables 0

Which of the following points (X,Y) is feasible?

(10,120)

(120,10)

(30,100)

(60,90)

none of the above


Maximize

5X + 6Y

Subject to:

4X + 2Y 420

1X + 2Y 120

all variables 0

Which of the following points (X,Y) is in the feasible region?

(30,60)

(105,0)

(0,210)

(100,10)

none of the above


Maximize

5X + 6Y

Subject to:

4X + 2Y 420

1X + 2Y 120

all variables 0

Which of the following points (X,Y) is feasible?

(50,40)

(30,50)

(60,30)

(90,20)

none of the above

Two models of a product Regular (X) and Deluxe (Y) are produced by a company. A linear programming model is used to determine the production schedule. The formulation is as follows:

Maximize profit

50X + 60Y

Subject to:

8X + 10Y 800 (labor hours)

X + Y 120 (total units demanded)

4X + 5Y 500 (raw materials)

all variables 0

The optimal solution is X = 100 Y = 0.

How many units of the labor hours must be used to produce this number of units?

400

200

500

120

none of the above

Unboundedness is usually a sign that the LP problem

has finite multiple solutions.

is degenerate.

contains too many redundant constraints.

has been formulated improperly.

none of the above.

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