Question

Kyle, a runner, is interested in mixing two cereals to minimize caloric intake while maintaining at least 96 units of calcium and 24 units of iron in each serving. Cheerios has 6 units of calcium, 3 units of iron and 14 calories per ounce. Fruitloops has 12 units of calcium, 2 units of iron and 11 calories per ounce. How much of each cereal should Kyle consume to minimize calorie intake while maintaining the minimum nutrient levels

Answer 1

Let x be the number of ounces Cheerios and y be ounce by Fruitloops.

Then, we have to minimize

$z= 14x+11y$

subject to $6x +12y\geq 96\ \ \ \Rightarrow \ x+2y\geq 16$

and $3x+2y\geq 24$

and $x,\ y\geq 0$

Here A, B, and C are corner points

A=(0,12)

C=(16,0)

and B is the intersection point of x+2y=16 and 3x+2y=24

On solving, we get x=4 and y=6

So, B=(4,6)

$\Rightarrow$ Z(A) = Z(0,12) = (14x0)+(11x12) = 132

$\Rightarrow$ Z(B) = Z(4,6) = (14x4 )+ (11x6)= 122

$\Rightarrow$ Z(C) = Z( 16,0)= (14x16)+(11x0)= 224

So, Z is minimum at B =(4,6)

$\Rightarrow 4$ ounce of Cheerios and $6$ ounce of Fruitloops are needed to minimize the calorie intake.