Bill's Grill is a popular college restaurant that is famous for its hamburgers. The owner of the restaurant, Bill, mixes fresh ground beef and pork with a secret ingredient to make delicious quarter-pound hamburgers that are advertised as having no more than 25% fat. Bill can buy beef containing 80% meat and 20% fat at $0.85 per pound. He can buy pork containing 70% meat and 30% fat at $0.65 per pound. Bill wants to determine the minimum cost way to blend the beef and pork to make hamburgers that have no more than 25% fat. Required:

1. What is objective function for the mathematical formulation, in words?

Explanation:

Given that:

Bill can buy  containing 80% meat and 20 % pound at $0.85 per pound

Also; He can buy pork containing 70% meat and 30% fat at $0.65 per pound.

Bill, mixes fresh ground beef and pork with a secret ingredient to make delicious quarter-pound hamburgers that are advertised as having no more than 25% fat.

From the information given:

The Objective is that Bill wants to determine the minimum cost way to blend the beef and pork to make hamburgers that have no more than 25% fat.

Also: Required is to find the  objective function for the mathematical formulation, in words.

Assumptions:

Let assume  that  should be the percentage of the beef.

Let assume  that  should be the percentage of the beef.

The buying cost of beef is  $0.85 and the buying cost of pork is $0.65

Hence; the Minimum Objective cost function for this model will be :

Also; from above:

We know that the fat in beef and pork is 20% and 30% respectively ( 0.2 and 0.3).

And Bill decided to make hamburgers that have fat not more than  25% (0.25)

Equally ; we can formulate a decision that the sum of the beef and pork should  be less than or equal to 0.25

So:

Since Bill is using both beef and pork for the production; there is need to add both entity together because He does not have to use either beef or pork alone;

So;

Of course , we know that the percentage of this aftermath result can't be zero. i.e it is definitely greater than 1.

So;

Thus; the Objective function of this model is :

  which is subjected to  

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