Ch13 Evans BA1e

8/10/2019 Ch13 Evans BA1e

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Decision Variables: How many of each model to produce (L LaserStop and S Speed MAX

Objective: Maximize Profit ST

Constraints: Availability of A

Availability of B

LaserStop SpeedBuster

Numbers Produced - 333.33 TOTAL PROFIT

Unit Profit 24.00$ 40.00$ 13,333.33$

Required A 18 12 4000


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Microsoft Excel 12.0 Answer Report

Worksheet: [Ch13 Solutions.xlsx]13.1 and 5

Report Created: 1/21/2012 2:05:09 PM

Target Cell (Max)

Cell Name Original Value Final Value$G$10 Unit Profit TOTAL PROFIT 13,333.33$ 13,333.33$

Adjustable Cells

Cell Name Original Value Final Value

$C$9 Numbers Produced LaserStop - -

$D$9 Numbers Produced SpeedBuster 333.33 333.33

Constraints

Cell Name Cell Value Formula Status Slack

$E$12 Required A 4000 $E$12


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Decision Variables: How many minutes of each type of ad should be purchased (R radio, T TV)

Objective: Maximize Exposure

Constraints: Limited Budget of $25,000

TV allocation should be at least 70%

Radio TV

Numbers Produced - 12.50 TOTAL EXPOSURE

Unit Exposure 150 800 10,000

Budget 400.00$ 2,000.00$ 25,000.00$ = 0 units avail


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MAX 150 R + 800 T

ST

400 R + 2000 T = 0.7 ( R + T)

R, T >= 0

Slack

BINDING 0

ble -3.75


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Worksheet: [Ch13 Solutions.xlsx]13.2


Target Cell (Max)

Cell Name Original Value Final Value$G$10 Unit Exposure TOTAL EXPOSURE 10,000 10,000

Adjustable Cells


$C$9 Numbers Produced Radio - -

$D$9 Numbers Produced TV 12.50 12.50

Constraints


$E$12 Budget 25,000.00$ $E$12=$G$13 Not Binding 3.75


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Decision Variables: How many of each type of desk to produce (S Standard, D Delu

Objective: Maximize Profit

Constraints: Availability of pine

Availability of oak

Availability of labor

Standard Deluxe

Numbers Produced - 25.00

Unit Profit 150.00$ 320.00$

Required Pine 80 60 1500


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xe) MAX 150 S + 320 D

ST

80 S + 60 D


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Target Cell (Max)

Cell Name Original Value Final Value$G$10 Unit Profit TOTAL PROFIT 8,000.00$ 8,000.00$

Adjustable Cells


$C$9 Numbers Produced Standard - -

$D$9 Numbers Produced Deluxe 25.00 25.00

Constraints


$E$12 Required Pine 1500 $E$12


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Decision Variables: How much money to invest in each stock, A, B,

Objective: Maximize total return

Constraints: Total investment money available

A B C

Shares Purchased 100.00 - -

Unit Return 12.00$ 7.00$ 12.00$

Price Per Stock 25.00$ 15.00$ 40.00$ 2500


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MAX 12 A + 7 B + 12 C

ST 25 A + 15 B + 40 C = 0

TOTAL RETURN

1,200.00$

Slack

2,500.00$ units available BINDING 0


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Target Cell (Max)

Cell Name Original Value Final Value$H$10 Unit Return TOTAL RETURN 1,200.00$ 1,200.00$

Adjustable Cells


$C$9 Shares Purchased A 100.00 100.00

$D$9 Shares Purchased B - -

$E$9 Shares Purchased C - -

Constraints


$F$12 Required A 2500 $F$12


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MAX 24 L + 40 S

ST

18 L + 12 S


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0 100 200 300 400 500 600 700

L

Constraint 1

Constraint 2Feasible

Regi

on


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MAX 150 R + 800 T

ST

400 R + 2000 T = 0.7 ( R + T) Constraint 2

R, T >= 0

400 2000 25000 62.5 0

0 12.5

0.3 -0.7 0 0 0

35 15

3rd corner of the feasible region 20 8.5


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0

2

4

6

8

10

12

14

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0 10 20 30 40 50 60 70

TV

Radio

Constraint 1

Constraint 2


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MAX 150 S + 320 D

ST

80 S + 60 D


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10 20 30 40 50 60 70 80

Standard

Constraint 1

Constraint 2

Constraint 3


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A B C D E F G

INDIVIDUAL ANSWERS MAY VARY

ORIGINAL

MAX 24 L + 40 S

ST

18 L + 12 S = 4000

06 L + 10 S >= 3500

would make the problem unbounded

c.

18 L + 12 S = 3500

would make the problem infeasible.


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1

2

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4

5

67

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A B C D E F G

INDIVIDUAL ANSWERS MAY VARY

ORIGINAL

MAX 150 R + 800 T

ST

400 R + 2000 T = 0.7 ( R + T)R, T >= 0

a.

MAX 200 R + 1000 T would give alternative optimal solutions

b.

400 R + 2000 T >= 25000

T >= 0.7 ( R + T)

would make the problem unbounded

c.

400 R + 2000 T = 0.7 ( R + T)

T>=15

would make the problem infeasible.


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A B C

Shares Purchased 100.00 - -

Unit Return 12.00$ 7.00$ 12.00$

Price Per Stock 25.00$ 15.00$ 40.00$ 2500


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TOTAL RETURN

1,200.00$

2,500.00$ units available


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a. (-0.3) means if the gross margin of plugs goes up by 0.30, we may start making plugs.

b. If gross margin for rails is decreased to $1.05, the optimal solution does not change (since the allo

c. If gross margin for rivets is increased to $0.85, the optimal solution does not change (since the all

d. If gross margin for clips is decreased to $1.10, the optimal solution will not change (since the allo

If gross margin for clips is decreased to $1.00, the optimal solution may change but we cannot predi

e. If machine capacity increases by 500 minutes, the optimal solution may change (we can't predict

If machine capacity decreases by 300 minutes, , the optimal solution may change (we can't predict h


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wable decrease is infinity)

wable increase is $0.15)

able decrease is more than 15 cents)

ct how.

ow much). Optimal profit will go up by 500 * 0.6

ow much). Optimal profit will go down by 300 * 0.6


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a. The reduced cost of SpeedBuster is 0, since we are already making some of it.

b. If the unit profit for LaserStop goes down to $20, the optimal solution does not change.

c. If the unit profit for LaserStop goes uo to $64, the optimal solution may change since $4

d. If 1000 more As are available, the optimal profit will go up but we cannot predict by how

e. If only 3000 Bs are available, the optimal profit will go down but we cannot predict by h


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(change) is more than the alloweable increase.

much.

w much.


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a. If exposure for TV goes up to 875, the optimal solution will remain the same and total ex

b. If radio exposure goes down to 150, the optmal solution will change - since a decrease of

c. If the budget goes up by $5000, the optimal exposure will go up by 5000 * 0.44

d. Because the shadow price tells you how one unit change in the RHS of a constraint affect


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posure will go up.

200 is more than the allowable decrease.

s the optimal objective function value within the range of optimality.


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a. If the profit for Standard Desks goes up by $50 or more, then it would become profitable to make

b. 25% is 187.5 square feet which is less than the allowable decrease which means we can predict h

Since the shadow price of this constraint is 0, nothing will change.

c. The shadow price of the labor constraint is $20, which means the next 266 hours of labor will incrSo overtime premium of $12 is ok.

d. A $20 decrease in the Deluxe desk profit is within the range of optimality, the optimal solution wil

The optimal profit will go down by $20 * 25.

e. Because they are not profitable enough. See (a) for when to produce them.


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Standard desks.

ow the profit will be affectedf.

ease the profit by $20/hour.

ll remain the same.


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a. It needs to go up to $7.2 per share.

b. It needs to go up to $19.2 per share.

c. Since the shadow price is $.48, every additional dollar invested in A will bring 48%.

So the student should borrow $1000 at 8% per year.


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J D

Numbers Produced 5.25 10.50 TOTAL PROFIT

Unit Profit 50.00$ #NAME? #NAME?

Fabrication 3.5 4 60.375


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LaserStop SpeedBuster

Numbers Produced - 333.33 TOTAL PROFIT

Unit Profit 24.00$ 40.00$ 13,333.33$

Required A 18 12 4000


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units availableunits available

Documents

Ch13 Evans BA1e