Question

The answer is C, but how do you get it?

The high school band wants to sell two types of cookies, chocolate chip and peanut butter, as a fundraiser. A dozen chocolate chip cookies requires 2 cups of flour and 1 egg. A dozen peanut butter cookies uses 3 cups of flour and 4 eggs. The club has 90 cups of flour and 80 eggs on hand. The profit on the chocolate chip cookies is $1 per dozen and on the peanut butter is $1.50 per dozen. If they want to offer both types of cookies, how many of each cookie should the club make to maximize profits?

Answer 1

a.
infeasible solutions

b.
30 dozen chocolate chip
25 dozen peanut butter

c.
24 dozen chocolate chip
14 dozen peanut butter

d.
20 dozen chocolate chip
18 dozen peanut butter

Answer 2

Name, Quantize, and Translate!

C = Number of Dozens Chocolate Chip Cookies (2 flour 1 egg)
P = Number of Dozens Peanut Butter Cookies (3 flour 4 eggs)

"90 cups of flour"

2C + 3P <= 90

"80 eggs"

C + 4P <= 80

"profit on the chocolate chip cookies is $1 per dozen and on the peanut butter is $1.50 per dozen"

Profit C(1.00) + P(1.50)

You just have to drag through it. There is no perfect way. They way you think about it that you understand is the way you should proceed.

Answer 3

So you can graph the equations for the eggs and flour
2C + 3P <= 90
C + 4P <= 80

and of their vertices that fall in quadrant 1, you can plug those coordinates into the equation C(1.00) + P(1.50) and that will get you the answer C, right?

Tell me if what I typed is confusing.

Answer 4

I think you have it. Just show a little more fortitude and read the problem very carefully. There is a LOT of information.