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  

a and c

explanation:

answer; ///(d); determining who competes most closely   with whom evaluating whether industry driving forces and competitive pressure favor some strategic groups and hurt others, and ascertaining whether the profit potential of different strategic groups varies due to the strengths and weaknesses in each groups respective market positions;