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Linear Programming Quiz

Total questions: 42

Worksheet time: 21mins

Name
Class
Date
1.

While plotting constraints on a graph paper, terminal points on both the axes are connected by a straight line because

a)

The resources are limited in supply.

b)

The objective function is a linear function.

c)

The constraints are linear equations or inequalities.

d)

All of the above.

2.

The distinguishing feature of an LP model is

a)

Relationship among all variables is linear.

b)

It has single objective function and constraints.

c)

Value of decision variables is nonnegative.

d)

All of the above.

3.

Which method is used for solving linear models?

a)

Graphical

b)

Simplex

c)

Solver

d)

All

4.

Acquiring input data is part of:

a)

model identification

b)

model formulation or solution

c)

model interpretation

d)

model testing

5.

A decision model has the following input variables: Historical sales data and historical advertising budget. The model is considered to be probabilistic.

a)

TRUE

b)

FALSE

6.

In dealing with business models, managers need to consider only quantitative data while making decisions in practice.

a)

TRUE

b)

FALSE

7.

Consider the following linear programming model.Min 2X1 + 3X2 Subject to: X1 + X2 ≥ 4, X1 ≥ 2, X1, X2 ≥ 0. This linear programming model has:

a)

unique optimal solution

b)

unbounded solution

c)

infeasible solution

d)

alternate optimal solution

8.

A linear programming model has the following two constraints: X1 ≥ 3 and X1 ≥ 4. This model has a redundant constraint.

a)

TRUE

b)

FALSE

9.

A linear programming problem has the following two constraints: X1 ≤ 20 and X1 ≥ 25. This problem is infeasible.

a)

TRUE

b)

FALSE

10.

When using Solver, the parameter Changing Cells is typically associated with the objective function.

a)

TRUE

b)

FALSE

11.

Surplus is typically associated with which type of constraints?

a)

≤

b)

≥

c)

=

d)

≠

12.

Corresponding to each dual there exists a primal

a)

TRUE

b)

FALSE

13.

The number of constraints in dual is equal to number of variables in primal.

a)

TRUE

b)

FALSE

14.

For converting a problem in to dual, minimization primal should have

a)

all constraints greater than equal to

b)

all constraints less than equal to

c)

all constraints equal to

d)

none of these

15.

Solution of primal cannot be read from dual.

a)

TRUE

b)

FALSE

16.

For converting a problem in to dual, all RHS of constraints should be

a)

non negative in case of minimization primal

b)

non negative in case of maximization primal

c)

both A and B

d)

none of these

17.

If all the values of the input variables in a decision model are random in nature, then the model is considered to be probabilistic.

a)

TRUE

b)

FALSE

18.

In the linear programming formulation of the transportation problem, cost of transporting one unit of the material from a supply point to a demand point appears in

a)

the objective function only.

b)

the constraints only.

c)

both objective function and constraints.

d)

neither objective function nor constraints.

19.

A baker uses organic flour from a local farmer in all of his baked goods. For each batch of bread (x1), he uses 4 pounds of flour. For a batch of cookies (x2), he uses 3 pounds, and for a batch of muffins (x3) he uses 2 pounds. The local farmer can supply him with no more than 24 pounds per week. The constraint that represents this condition is:

a)

x1 = 8, x2 = 8, x3 = 8.

b)

x1 + x2 + x3 = 24.

c)

x1 + x2 + x3 = 24.

d)

4x1 + 3x2 + 2x3 = 24.

20.

It's time to buy pet food again and Lisa heads to the grocery store with $40 in her purse, leaving her seven hungry cats and four hungry dogs at home. Dog food costs $1 per can and cat food costs $0.50 per can. Dogs eat two full cans of food each day but cats eat only one can. Lisa would like to buy enough food to last through her three-day weekend. What is one appropriate constraint for this scenario?

a)

7C + 4D = 3

b)

1C + 2D = 40

c)

.5C + 1D = 40

d)

7C + 4D = 1.5

21.

Larry's Fish Market buys salmon (S) for $5 per pound and a local whitefish (W) for $3.50 per pound. Larry wants to minimize his cost, but he cannot spend more than $160. The objective function that minimizes these costs for Larry is:

a)

5S + 3.5W = 160.

b)

Min 5S + 3.5 W.

c)

Max 5S + 3.5 W.

d)

Min 5S + 3.5W = 160.

22.

Which of the following statements about infeasible problems is best?

a)

All of the possible solutions violate at least one constraint.

b)

All of the possible solutions violate all of the constraints.

c)

At least one of the possible solutions violates all of the constraints.

d)

At least one of the possible solutions violates at least one of the constraints.

23.

The production manager for the Coory soft drink company is considering the production of two 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 the 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?

a)

90R and 75D

b)

135R and 0D

c)

75R and 90D

d)

40R and 100D

24.

Converting a transportation problem LP from cost minimization to profit maximization requires only changing the objective function; the conversion does not affect the constraints.

a)

True

b)

False

25.

A transportation problem with three sources and four destinations will have seven decision variables.

a)

True

b)

False

26.

and four destinations will have seven decision variables.

a)

True

b)

False

27.

The assignment problem is a special case of the transportation problem in which one agent is assigned to one, and only one, task.

a)

True

b)

False

28.

In a transportation problem with total supply equal to total demand, if there are four origins and seven destinations, and there is a unique optimal solution, the optimal solution will utilize 11 shipping routes.

a)

True

b)

False

29.

The objective of the transportation problem is to

a)

Identify one origin that can satisfy total demand at the destinations and at the same time minimize total shipping cost.

b)

Minimize the number of origins used to satisfy total demand at the destinations.

c)

Minimize the number of shipments necessary to satisfy total demand at the destinations.

d)

Minimize the cost of shipping products from several origins to several destinations.

30.

Impact of changes in RHS values of constraints is typically measured by the:

a)

reduced cost

b)

RHS allowable increase value

c)

RHS allowable decrease value

d)

shadow price

31.

A constraint has a slack of 5 units. This implies that:

a)

this constraint has exceeded its minimal requirement by 5 units

b)

this constraint has consumed 5 units of its resource

c)

this constraint has a surplus of 5 units

d)

this constraint is binding

e)

this constraint has 5 units of its resource unconsumed

32.

Assume that the shadow price of a non-binding "≤" constraint is 5. This implies that:

a)

if the right-hand side value of the constraint increases by 1 unit, the objective function value will increase by 5 units

b)

if the right-hand side value of the constraint increases by 1 unit, the objective function value will decrease by 5 units

c)

if the right-hand side value of the constraint increases by 1 unit, the objective function value will remain unchanged

d)

if the right-hand side value of the constraint decreases by 1 unit, the objective function value will increase by 5 units

33.

A section of output from The Management Scientist is shown: Variable1, Lower Limit=60, Current Value=100, Upper Limit=120. What will happen to the solution if the objective function coefficient for variable 1 decreases by 20?

a)

Nothing. The values of the decision variables, the dual prices, and the objective function will all remain the same.

b)

The value of the objective function will change, but the values of the decision variables and the dual prices will remain the same.

c)

The same decision variables will be positive, but their values, the objective function value, and the dual prices will change.

d)

The problem will need to be resolved to find the new optimal solution and dual price.

34.

A section of output from The Management Scientist is shown: Constraint2, Lower Limit=240, Current Value=300, Upper Limit=420. What will happen if the right-hand-side for constraint 2 increases by 200?

a)

Nothing. The values of the decision variables, the dual prices, and the objective function will all remain the same.

b)

The value of the objective function will change, but the values of the decision variables and the dual prices will remain the same.

c)

The same decision variables will be positive, but their values, the objective function value, and the dual prices will change.

d)

The problem will need to be resolved to find the new optimal solution and dual price.

35.

Which of the following is not a question answered by standard sensitivity analysis information?

a)

If the right-hand side value of a constraint changes, will the objective function value change?

b)

Over what range can a constraint's right-hand side value without the constraint's dual price possibly changing?

c)

By how much will the objective function value change if the right-hand side value of a constraint changes beyond the range of feasibility?

d)

By how much will the objective function value change if a decision variable's coefficient in the objective function changes within the range of optimality?

36.

With reference to the attached Spreadsheet screenshot, What is the cell formula for B17?

a)

=B12+C12

b)

=B4*B11+C4*C11

c)

=B5*B11+C5*C11

d)

=B6*B11+C6*C11

37.

Using this snippet of the sensitivity report for constraints, which of these conclusions is best?

a)

None of items Two, Three or Four is being used.

b)

Adding two units of One will increase the objective function value by two.

c)

Taking away four units of One will lower the objective function value by four.

d)

The most valuable resource is Four.

38.

Using this snippet of the sensitivity report for variable cells, which of these conclusions is best?

a)

Item A can drop in value all the way down to 1.25 before it harms the result.

b)

Items B and C are the only elements in the final model.

c)

The final value of this problem is 9.

d)

Insisting that one additional unit of B, be included in the model will reduce the profit by $2.

39.

If the optimal solution to the LP Relaxation problem is an integer, it is the optimal solution to the integer linear program.

a)

True

b)

False

40.

The constraint x1 + x2 + x3 + x4 ≤ 2 means that two out of the first four projects must be selected.

a)

True

b)

False

41.

The constraint x1 − x2 = 0 implies that if project 1 is selected, project 2 cannot be.

a)

True

b)

False

42.

If a problem has only less-than-or-equal-to constraints with positive coefficients for the variables, rounding down will always provide a feasible integer solution.

a)

True

b)

False