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60 / 63

1.25

2.00

1.75

0

0

0

Quantity

x1

x2

x3

s1

s2

s3

200

- 0.3

0

0

1

- 0.8

-2

500

1

0

1

0

1

1

500

0

1

0

0

0

1

1,875

1.75

2.00

1.75

0

1.75

3.75

- .5

0

0

0

- 1.75

- 3.75

A-60

Module A

The Simplex Solution Method

The optimal simplex tableau follows:

z j

c j - z j

c j

Basic Variables

0 1.75 2.00

s x x 1 3 2

  • a.

    Formulate the dual for this problem and define the dual variables.

  • b.

    Determine the optimal ranges for c1, c2, and c3.

  • c.

    Determine the range for q3 (ham salad sandwiches).

  • d.

    Overnight Foods is considering advertising its cheese sandwiches to increase demand. The company estimates that spending $100 on some leaflets that would be packaged with all other sandwiches would increase the demand for both kinds of cheese sandwiches by 200. Should it make this expenditure?

51. Given the linear programming model, minimize Z = 3x1 + 5x2 + 2x3 subject to

x 1 , x 2 , x 3 Ú 0 - x 1 + x 2 Ú 2 5 x 1 + 2 x 2 Ú 5 0 x 1 + x 2 - 3 x 3 Ú 3 5

and its optimal simplex tableau,

Basic Variables

Quantity

3 x1

5 x2

2 x3

0 s1

0 s2

0 s3

s x x

2 1 2

15 5 30

0 1 0

0 0 1

-4 -2 -1

-3>2 -1>2 -1>2

1 0 0

-1>2 1>2 -1>2

z

j

165

3

5

- 11

-4

0

-1

z -c

j

j

0

0

- 13

-4

0

-1

c j

0 3 5

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