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Week 5 Extra Problem Solutions

CHAPTER 5

WHAT-IF ANALYSIS FOR LINEAR PROGRAMMING

Problems

5.1.

Let T represent # of Toys and S represent #of Subassemblies.

Maximize:P=3T-2.5S

Subject to: 2T-S<=3000

T-S<=1000

T,S>=0

a)

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7

8

9

A B C D E F

Toys Subassemblies

Unit Profit $3.00 -$2.50

Used Available

Subassembly A 2 -1 3,000 <= 3,000

Subassembly B 1 -1 1,000 <= 1,000

Toys Subassemblies Total Profit

Production 2,000 1,000 $3,500

Resource Usage

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b)

Unit

Profit

Optimal

Production Rates

Total

for Toys

Toys

Subassemblies

Profit

$2.00

1000

0

$2000

$2.50

1000

0

$2500

$3.00

2000

1000

$3500

$3.50

2000

1000

$4500

$4.00

2000

1000

$5500

The estimate of the unit profit for toys can decrease by somewhere

between $0 and $0.50 before the optimal solution will change. There is no

change in the solution for an increase in the unit profit for toys (at least

for increase up to $1).

c)

Unit Profit

Optimal

Production Rates

Total

for

Subassemblies

Toys

Subassemblie

s

Profit

-$3.50

1000

0

$3000

-$3.00

1000

0

$3000

-$2.50

2000

1000

$3500

-$2.00

2000

1000

$4000

-$1.50

2000

1000

$4500

The estimate of the unit profit for subassemblies can decrease by

somewhere between $0 and $0.50 before the optimal solution will

change. There is no change in the solution for an increase in the unit

profit for subassemblies (at least for increases up to $1).

d) Parameter analysis report for change in unit profit for toys (part b):

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