Question

The Cookie Factory wants to sell chocolate chip and peanut butter cookies in combination packages of 6-12cookies. At least three of each type of cookie should be in each package. The cost of making a chocolatechip cookie is 19 cents, and the selling price is 44 cents each. The cost of making a peanut butter cookie is13 cents, and the selling price is 39 cents. How many of each type of cookie should be in each package tomaximize the profit?A. 3 chocolate chip and 3 peanut butter B. 3 chocolate chip and 9 peanut butterC. 9 chocolate chip and 3 peanut butter D. 0 chocolate chip and 12 peanut butter

Answer 1

Let the number of chocolate chip cookies sold=x

Let the number of peanut butter cookie sold =y

The cost of making a chocolate chip cookie is 19 cents, and the selling price is 44 cents each.

Therefore, the profit made on chocolate chip cookie

=44-19

=25 cents

=$0.25

The cost of making a peanut butter cookie is 13 cents, and the selling price is 39 cents.

Therefore, the profit made on peanut butter cookie

=39-13

=26 cents

=$0.26

Therefore, the profit made when x cookies and y cookies are sold will be:

P(x,y)=0.25x+0.26y

To determine how many of each type of cookie should be in each package to maximize the profit, we use the coordinates of the feasible region (which are given in the options).

Option A: x=3, y=3

P(x,y)=0.25(3)+0.26(3)=$1.53

Option B: x=3, y=9

P(x,y)=0.25(3)+0.26(9)=$3.09

Option C: x=9, y=3

P(x,y)=0.25(9)+0.26(3)=$3.03

Option D: x=0, y=12

P(x,y)=0.25(0)+0.26(12)=$3.12

Since the point (0,12) gives the highest value, 0 chocolate chip and 12 peanut butter cookies should be in each package to maximize the profit.