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[answered] A food processing company makes meatloaf to be sold in the


A food processing company makes meatloaf to be sold in the frozen food section of supermarkets. Each week the recipe used changes based on the current cost of ingredients. Ingredients and current costs are as shown below:

Ingredient Cost/pound

pork $2.87

hamburger $1.63

wheat filler $0.22

corn filler $0.16

For each batch made, at least 300 pounds of pork and 100 pounds of hamburger are required. No more than 200 pounds of wheat filler can be used per batch and the amount of corn filler has to range between 50 and 150 pounds. Moreover, each batch must contain at least 500 pounds of meat and no more than 200 pounds of filler. Develop the LP formulate for this problem.

ANSWER:

X1 = pounds of pork used; X2 = pounds of hamburger used

X3 = pounds of wheat used; X4 = pounds of corn used


FOOD PROCESSING INGREDIENTS MODEL

 

Pork

 

x1

 

300

 

Cost, $/lb Hamburger Wheat

 

x2

 

x3

 

200

 

0

 

2.87

 

1.63

 

0.22 Corn

 

x4

 

50

 

0.16 $ 1,195 Constraint

 

Pork

 

Hamburger

 

Wheat filler

 

Corn filler

 

Corn filler

 

Meat...

 


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