WKU MGT313 final exam 100% grade

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QUESTION 1

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

5 points Save Answer

QUESTION 2

When do alternate optimal solutions occur in LP models?

A.

When a binding constraint is parallel to a level curve.

B.

When a non-binding constraint is perpendicular to a level curve.

C.

When a constraint is parallel to another constraint.

D.

Alternate optimal solutions indicate an infeasible condition.

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QUESTION 3

A facility produces two products and wants to maximize profit. The objective function to maximize is z=350x1+300x2. The number 350 means that:

A.

one unit of product 1 contributes $350 to the objective function

B.

one unit of product 1 contributes $300 to the objective function

C.

the problem is unbounded

D.

the problem has no constraints

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QUESTION 4

The shadow price of a nonbinding constraint is

A.

positive

B.

zero

C.

negative

D.

indeterminate

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QUESTION 5

A production company wants to ensure that if Product 1 is produced, production of Product 1 not exceed production of Product 2. Which of the following constraints enforce this condition?

A.

X1 ≥ M2Y2

B.

X1 ≤ M2X2

C.

X1 ≤ M1Y1, X1 ≤ Y1X2

D.

X1 ≤ X2

5 points Save Answer

QUESTION 6

A change in the right hand side of a constraint changes

A.

the slope of the objective function

B.

objective function coefficients

C.

other right hand sides

D.

the feasible region

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QUESTION 7

If the shadow price of a constraint of a linear program is different from zero then the constraint is binding at the optimal solution.

True

False

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QUESTION 8

If one of the objective coefficients of a linear program changes, then the optimal solution must change.

True

False

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QUESTION 9

It is possible for the feasible region of a linear program to have exactly one point.

True

False

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QUESTION 10

It is possible for an integer linear program to have more than one optimal solution.

True

False

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QUESTION 11

Exhibit 3.3

The following questions, 15, 16, 17, are based on this problem and accompanying Excel windows.

Jack's distillery blends scotches for local bars and saloons. One of his customers has requested a special blend of scotch targeted as a bar scotch. The customer wants the blend to involve two scotch products, call them A and B. Product A is a higher quality scotch while product B is a cheaper brand. The customer wants to make the claim the blend is closer to high quality than the alternative. The customer wants 50 1500 ml bottles of the blend. Each bottle must contain at least 48% of Product A and at least 500 ml of B. The customer also specified that the blend have an alcohol content of at least 85%. Product A contains 95% alcohol while product B contains 78%. The blend is sold for $12.50 per bottle. Product A costs $7 per liter and product B costs $3 per liter. The company wants to determine the blend that will meet the customer's requirements and maximize profit.

Let X1 = Number of liters of product A in total blend delivered X2 = Number of liters of product B in total blend delivered

MIN: 7 X1 + 3 X2

Subject to: X1 + X2 = 1.5 * 50 (Total liters of mix)

X1 ≥ 0.48 * 1.5 * 50 (X1 minimum)

X2 ≥ 0.5 * 50 (X2 minimum)

.0.95 X1 + 0.78 X2 ≥ 0.85 * 1.5 * 50 (85% alcohol minimum) X1, X2 ≥ 0

A

B

C

D

E

1

Jacks' Distillery

2

3

A

B

4

Liters to use

Total Cost:

5

Unit cost:

10.5

4.5

6

7

Constraints:

Supplied

Requirement

8

Total Liters

1

1

75

9

A required

1

36

10

B required

1

25

11

85% alcohol

0.95

0.78

63.75

Refer to Exhibit 3.3. What formula should be entered in cell E5 in the accompanying Excel spreadsheet to compute total cost?

A.

=B4*C4+B5*C5

B.

=SUMPRODUCT(B4:C4,B5:C5)

C.

=SUM(B5:C5)

D.

=SUM(E8:E10)

5 points Save Answer

QUESTION 12

Refer to Exhibit 3.3. What formula should be entered in cell D11 in the accompanying Excel spreadsheet to compute the total liters of alcohol supplied?

A.

=B4*B5+C4*C5

B.

=SUMPRODUCT(B11:C11,$B$4:$C$4)

C.

=SUM(B5:C5)

D.

=SUM(E8:E10)

5 points Save Answer

QUESTION 13

Refer to Exhibit 3.3. Which cells should be changing cells in this problem?

A.

B4:C4

B.

E5

C.

D8:D10

D.

E8:E10

5 points Save Answer

QUESTION 14

Which formula should be used to determine the Net Flow values in cell K6 in the following spreadsheet model?

A

B

C

D

E

F

G

H

I

J

K

L

1

2

3

4

Supply/

5

Ship

From

To

Unit Cost

Nodes

Net Flow

Demand

6

55

1

LAV

2

PHO

60

1

LAV

−100

−100

7

45

1

LAV

4

REN

120

2

PHO

50

50

8

5

2

PHO

3

LAX

160

3

LAX

30

30

9

0

3

LAX

5

SAN

70

4

REN

45

45

10

25

5

SAN

3

LAX

90

5

SAN

90

90

11

0

5

SAN

4

REN

70

6

DEN

35

35

12

0

5

SAN

6

DEN

90

7

SLC

−150

−150

13

0

6

DEN

5

SAN

50

14

0

7

SLC

4

REN

190

15

115

7

SLC

5

SAN

90

16

35

7

SLC

6

DEN

100

17

18

Total

25600

A.

SUMIF($C$6:$C$16,I6,$B$6:$B$16)−SUMIF($E$6:$E$16,I6,$B$6:$B$16)

B.

SUMIF($I$6:$I$12,B6,$B$6:$B$16)−SUMIF($I$6:$I$12,I6,$B$6:$B$16)

C.

SUMIF($E$6:$E$16,I6,$B$6:$B$16)−SUMIF($C$6:$C$16,I6,$B$6:$B$16)

D.

SUMPRODUCT(B6:B16,G6:G16)

5 points Save Answer

QUESTION 15

A company is developing its weekly production plan. The company produces two products, A and B, which are processed in two departments. Setting up each batch of A requires $60 of labor while setting up a batch of B costs $80. Each unit of A generates a profit of $17 while a unit of B earns a profit of $21. The company can sell all the units it produces. The data for the problem are summarized below.

Hours required by

Operation A B Hours

Cutting 3 4 48

Welding 2 1 36

The decision variables are defined as

Xi = the amount of product i produced

Yi = 1 if Xi > 0 and 0 if Xi = 0

Which of the following constraints creates the link between setting up to produce A's and making some A's for this problem?

A.

X1 ≤ 16Y1

B.

X1 − Y1 = 0

C.

X1 − 18Y1 > 0

D.

= if(X1 > 0, Y1 = 1, Y1 = 0)

5 points Save Answer

QUESTION 16

A wedding caterer has several wine shops from which it can order champagne. The caterer needs 100 bottles of champagne on a particular weekend for 2 weddings. The first supplier can supply either 40 bottles or 90 bottles.

The relevant decision variable is defined as

X1 = the number of bottles supplied by supplier 1

Which set of constraints reflects the fact that supplier 1 can supply only 40 or 90 bottles?

A.

X1 ≤ 40 Y11, X1 ≤ 90(1 − Y11)

B.

X1 = 40Y11 + 90Y12, Y11 + Y12 ≤ 1

C.

X1 = 40Y1 + 90(1 − Y1), Y1 = 0 OR 1

D.

X1 = 40Y11 + 90Y12, Y11 + Y12 = 1

5 points Save Answer

QUESTION 17

The optimal relaxed solution for an ILP has X1 = 3.6 and X2 = 2.9. If we branch on X1, what constraints must be added to the two resulting LP problems?

A.

X1 ≥ 3, X1 ≥ 4

B.

X1 = 4

C.

3 ≤ X1, X1 ≤ 4

D.

X1 ≤ 3, X1 ≥ 4

5 points Save Answer

QUESTION 18

A company wants to locate a new warehouse to minimize the distance traveled by its delivery trucks. It has four stores and their coordinates are listed in the accompanying spreadsheet. Which cell(s) in the spreadsheet represent the decision variables in the problem?

A

B

C

D

1

2

X-Coordinate

Y-Coordinate

3

Warehouse

163.800

101.000

Distance:

4

Store 1

100

130

70.082

5

Store 2

90

60

84.424

6

Store 3

210

80

50.749

7

Store 4

180

110

18.532

8

9

Total Distance:

223.787

A.

B3

B.

B3:C3

C.

B4:C7

D.

D9

5 points Save Answer

QUESTION 19

An office supply company is attempting to determine the order quantity for laser printer toner cartridges, which are sold to local businesses. Annual demand is 20,000 units and each cartridge costs the store $25. It costs $30 to place an order and the inventory carrying cost rate is 25% of the value of the item. The following spreadsheet has been set up to solve the problem. What cell is the variable cell in this problem?

A

B

1

2

3

Annual Demand:

20,000

4

5

Cost per Unit:

$25

6

Ordering Cost:

$30

7

Carrying Cost:

25%

8

9

Order Quantity:

483.73

10

11

Total Cost:

$502,738.61

A.

B3

B.

B7

C.

B9

D.

B11

5 points Save Answer

QUESTION 20

Limited resources are modeled in optimization problems as

A.

an objective function.

B.

constraints.

C.

decision variables.

D.

alternatives.

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QUESTION 21

A manager has only 200 tons of plastic for his company. This is an example of a(n)

A.

decision.

B.

constraint.

C.

objective.

D.

parameter.

5 points (Extra Credit) Save Answer

QUESTION 22

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.

5 points (Extra Credit) Save Answer

QUESTION 23

If the allowable increase for a constraint is 100 and we add 110 units of the resource what happens to the objective function value?

A.

increase of 100

B.

increase of 110

C.

decrease of 100

D.

increases but by unknown amount