Question

A dog breeder plans to mix two types of food to make a mix of low cost

feed for his puppies. A bag of ChowChow costs $10 and contains 40 units
of proteins, 20 units of minerals and 10 units of vitamins. A bag of Kibble
costs $12 and contains 30 units of proteins, 20 units of minerals and 30
units of vitamins. How many bags of ChowChow and Kibble should he
feed the puppies each day in order to meet the minimum daily
requirements of 150 units of proteins, 90 units of minerals and 60 units of
vitamins at a minimum cost?

Answer 1

• 3.75 bags of ChowChow
• 0.75 bags of Kibble

Explanation:

The constraints on protein, minerals, and vitamins give rise to the inequalities ...

40c +30k ≥ 150 . . . . . . required protein

20c +20k ≥ 90 . . . . . . required minerals

10c +30k ≥ 60 . . . . . . . required vitamins

And we want to minimize 10c +12k.

The graph shows the vertices of the feasible region in (c, k) coordinates. The one that minimizes cost is (c, k) = (3.75, 0.75).

To minimize cost, the daily feed should be ...

• 3.75 bags of ChowChow
• 0.75 bags of Kibble

Daily cost will be $46.50.