Question

A chocolate bar contains 50 calories and s of protein and makes a

child smile 7 times while eating it. A granota bar contains 25 calories and
15 grams of protein and makes a child smile 2 times while eating it. A
teacher plans to serve some of these snacks to his first grade class. They
should total at least 40 grams of protein and no more than 150 calories.
How many of each kind of bar should he serve to maximize smiles?

Answer 1

He should serve 2 chocolate bars and 2 granola bars

Explanation:

Let's define

x: amount of chocolate bar

y: amount of granola bar

We are asked to solve the following optimization problem:

maximize 7*x + 2*y

subject to

50*x + 25*y ≤ 150

5*x + 15*y ≥ 40

x ≥ 0

y ≥ 0

In the figure attached, the feasible region is shown. The solution is one of the vertex

vertex objective function

(0, 2.667) 7*0 + 2*2.667 = 5.334

(2, 2) 7*2 + 2*2 = 18

(0, 6) 7*0 + 2*6 = 12