Mr Smith decides to feed his pet Doberman pinscher a combina

Mr. Smith decides to feed his pet Doberman pinscher a combination of two dog foods. Each can of brand A contains 4 units of protein, 1 unit of carbohydrates, and 2 units of fat and costs 80 cents. Each can of brand B contains 1 unit of protein, 1 unit of carbohydrates and 4 units of fat and costs 40 cents. Mr. Smith feels that each day his dog should have at least 8 units of protein, 5 units of carbohydrates and 16 units of fat. How many cans of each dog food should he give to his dog each day to provide the iminimum requirements at the least cost?

Solution

Given that Mr. Smith has a dog and he used to feed the dog with a  combination of two dog foods.

Brand A contains 4 units of protein, 1 unit of carbohydrates, and 2 units of fat and costs 80 cents.

Brand B contains 1 unit of protein, 1 unit of carbohydrates and 4 units of fat and costs 40 cents.

Each day his dog should have at least 8 units of protein, 5 units of carbohydrates and 16 units of fat.

Need to find out the number of cans of each brand to feed the dog at least 8 units of protein, 5 units of carbohydrates and 16 units of fat at the least cost.

By making some trials to find the minimum cost for the dog feed,

It is found that 1 can of brand A and 4 cans of brand B satisfies the given conditions.

1 can of brand A contains 4 units of protein, 1 unit of carbohydrates, and 2 units of fat

4 cans of brand B conyains 4 units of protein, 4 unit of carbohydrates, and 16 units of fat

A total of 8 units of protein, 5 unit of carbohydrates, and 18 units of fat .

And the cost of combination of two dog foods=1*80+4*40

= 80+160

= 240 cents.

Therefore, Mr.Smith has to give 1 can of brand A and 4 cans of brand B to his dog each day to provide the minimum requirements at the least cost 240 cents.