Answer:
24 dozen chocolate chip
14 dozen peanut butter
Step-by-step explanation:
x = number of dozen chocolate chip cookies
y = number of dozen peanut butter cookies
Total number of cups of flour is:
2x + 3y ≤ 90
Total number of eggs is:
x + 4y ≤ 80
Total profit is:
P = x + 1.5y
Since this is multiple choice, one method would be to calculate the profit for each option, then choose the one that's largest.
But let's try solving this algebraically. x and y are positive integers, and we want them to be as large as possible.
Let's start by assuming the solution is on the line 2x + 3y = 90.
x + 4y ≤ 80
2x + 8y ≤ 160
90 − 3y + 8y ≤ 160
5y ≤ 70
y ≤ 14
If y = 14, x = 24, and P = 45.
Now let's assume the solution is on the line x + 4y = 80.
2x + 3y ≤ 90
2 (80 − 4y) + 3y ≤ 90
160 − 8y + 3y ≤ 90
70 ≤ 5y
14 ≤ y
Therefore, to maximize the profit, they should bake 24 dozen chocolate chip cookies and 14 dozen peanut butter cookies.
