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A-48

Module A

The Simplex Solution Method

maximize Z = 5x1 + 4x2 (profit, $)

subject to

( y a r n , y d . ) x 1 , x 2 Ú 0 1 0 x 1 + 4 x 2 2 , 0 0 0 0 . 3 x 1 + 0 . 5 x 2 1 5 0 ( l e a t h e r , f t . 2 )

Solve this model using the simplex method.

18. A clothing shop makes suits and blazers. Three main resources are used: material, rack space, and labor. The shop has developed this linear programming model for determining the number of suits and blazers to make (x1 and x2) to maximize profits:

maximize Z = 100x1 + 150x2 (profit, $) subject to

( r a c k s p a c e ) ( l a b o r , h r . ) x 1 , x 2 Ú 0 1 0 x 1 + 2 0 x 2 3 0 0 x 1 + x 2 2 0 1 0 x 1 + 4 x 2 1 6 0 ( m a t e r i a l , y d . 2 )

Solve this model using the simplex method. 19. Solve the following linear programming model using the simplex method: maximize Z = 100x1 + 20x2 + 60x3

subject to

1

2

-1

0 s1

0 s2

0 s3

x1

x2

x3

0 0 1

1 0 0

1/4 -3>4 1

1/4 3/4 -1>2

0 1 0

0 -1>2 1/2

1

2

3/2

0

0

1/2

0

0

-5>2

0

0

-1>2

20. The following is a simplex tableau for a linear programming model:

  • a.

    Is this a maximization or a minimization problem? Why?

  • b.

    What is the solution given in this tableau?

  • c.

    Write out the original objective function for the linear programming model, using only

decision variables.

  • d.

    How many constraints are in the linear programming model?

  • e.

    Were any of the constraints originally equations? Why?

  • f.

    What does s1 equal in this tableau?

2 2x1 + 2x + 2x

3

x

3

x1, x2, x

3

30

3 x 1 + 5 x

2

  • 60

  • 100

  • 40

Ú0

Quantity

10 20 10

z j

c j - z j

c j

Basic Variables

2 0 1

x s x 2 2 1

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