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Problems

A-55

  • a.

    Formulate the dual of this model and indicate what the dual variables equal.

  • b.

    What profit for Razorback chili will result in no production of Longhorn chili? What will

the new optimal solution values be? c. Determine what the effect will be of changing the amount of beans in Razorback chili from

10 pounds per batch to 15 pounds per batch. d . D e t e r m i n e t h e o p t i m a l r a n g e s f o r a n d e . D e t e r m i n e t h e f e a s i b l e r a n g e s f o r ( p o u n d s o f b e a n s ) a n d ( p o u n d s o f g r o u n d b e e f ) . q 2 q 1 c 2 . f. What is the maximum price the company would be willing to pay for additional pounds of c 1

chili beans, and how many pounds could be purchased at that price? g. If the company could secure an additional 100 pounds of only one of the ingredients, beans

or ground beef, which should it be? h. If the company changed the selling price of Longhorn chili so that the profit was $400

instead of $300, would the optimal solution be affected?

44. The Agrimaster Company produces two kinds of fertilizer spreaders—regular and cyclone. Each spreader must undergo two production processes. Letting x1 = the number of regular spreaders produced and x2 = the number of cyclone spreaders produced, the problem can be formulated as follows:

maximize Z = 9x1 + 7x2 (profit, $)

subject to

( p r o c e s s 1 , p r o d u c t i o n h r . ) ( p r o c e s s 2 , p r o d u c t i o n h r . ) x 1 , x 2 Ú 0 4 x 1 + 8 x 2 4 0 1 2 x 1 + 4 x 2 6 0

The final optimal simplex tableau for this problem is as follows:

9

7

0

0

x1

x2

s1

s2

1

0

1>10

-1>20

0

1

-1>20

3>20

9

7

11>20

12>20

0

0

-11>20

-12>20

c j

9 7

57

c j - z j z j

x

1

x

2

Basic Variables

Quantity

4 3

a. Formulate the dual for this problem. b. Define the dual variables and indicate their values. c . D e t e r m i n e t h e o p t i m a l r a n g e s f o r a n d d . D e t e r m i n e t h e f e a s i b l e r a n g e s f o r a n d ( p r o d u c t i o n h o u r s f o r p r o c e s s e s 1 a n d 2 , q 2 q 1 c 2 . c 1

respectively). e. What is the maximum price the Agrimaster Company would be willing to pay for

additional hours of process 1 production time, and how many hours could be purchased at that price?

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