a kennel mixes brands of dog food.brand x costs 25 dollars and brand y costs 20 dollars.

Question

brand x has 2 carbs 2 fat and 2 protein. brand y has 1 carb 9 fat and 3 protein. the minimum of carbs are 12 min. of 36 fats and a min. of 24 protein. how many bags of each should be mixed to minimize cost and what is that cos

Answer 1

Say, cost per bag for x brand =25$

       cost per bag for y brand = 20$

 

So, we need to minimize z = (25x+20y) 

If we further formulate the problem,

The given constraints are---

 

2x+y. equal or < 12

2x+9y equal or < 36

2x+3y equal or < 24

 

Making a graphical plot of the constraints

The corner points are

(0,0)

(6,0)

(0,4)

(9/2,3)

Checking the value of z at all these corner points

 

Minimum z occurs at (0,4)

Value of z ( minimum cost ) =80$