1. ## Linear Programming

Craig Browning bakes cookies for the elementary school cookie sale. His chocolate chip cookies sell for $1.00 a dozen, and his oatmeal brownie cookies sell for$1.50 per dozen. He will bake up to 20 dozen chocolate chip cookies, and up to 40 dozen oatmeal brownie cookies, but no more than 50 dozen cookies total. Also, the number of oatmeal brownie cookies will be no more than three times the number of chocolate chip cookies. How many of each kind should Craig make in order to make the most money? How much will this be?

a. Define each variable and write the constraints for this problem

For this I did:

let x = chocolate chip
let y = oatmeal brownie cookies

My constraints:

x + y ≤ 50
x ≤ 20
y ≤ 40
x ≤ 3y

Those were my constraints but when I went to graph them, it did not seem right. Unless I graphed them wrong.

2. If R=revenue, then the constraint to optimize would be $\displaystyle x+1.5y=R$

$\displaystyle x+y\leq 50$

$\displaystyle x\leq 20$

$\displaystyle y\leq 40$

$\displaystyle y\leq 3x$

Graphing we find several points to check. I think (10,40) is the one we need.

10 chocolate chip and 40 oatmeal.

Is that what you get?.

Plug them into the constraint to find which is the highest.

3. I will plug them into the constraint in a second but. What I would like to make sure is, are my constraints correct?