Gerber Products Gerber Mixed Cereal for Baby contains in eac

Gerber Product\'s Gerber Mixed Cereal for Baby contains, in each serving, 60 calories and 11 grams of carbohydrates. Gerber Mango Tropical Fruit Dessert contains, in each serving, 80 calories and 21 grams of carbohydrates. If the cereal costs 32¢ per serving and the dessert costs 50¢ per serving, and you want to provide your child with at least 140 calories and at least 32 grams of carbohydrates, how can you do so at the least cost? (Fractions of servings are permitted. If an answer does not exist, enter DNE.) Gerber Mixed Cereal for Baby serving(s) Gerber Mango Tropical Fruit Dessert serving(s)

Solution

First let us tabulate the given data

Let x cereals and y desserts be used

Then constraints are 60x+80y >=140 and 11x+21y>=32

Simplify to get 3x+4y>=7 and 11x+21y>=32

Multiply I equation by 11 and second by 3

33x+44y>=77 and

33x+63y>=96

Subtract 19y>=19

y >=1 and x>=1

Hence atleast one Gerber Mixed Cereal for Baby serving(s) and one Gerber Mango Tropical Fruit Dessert serving(s)

should be given to child.