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?

The number of chocolate chip cookies are: 288 cookies.

Number of peanut butter cookies are: 168 cookies.

Step-by-step explanation:

Let x denote the number of dozen chocolate chip cookies.

Let y denote the number of dozen peanut butter cookies.

Now is is given that:

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.

Also,

The club has 90 cups of flour and 80 eggs on hand.

Hence, the inequality that can be formed with the help of these information is:

                  2x+3y≤90

     and      x+4y≤80

Also, the objective function is:

         Max.   z=x+1.50y  

where z is the profit function which is to be maximized.

Hence, on solving we get boundary point at:

(0,0) ,(45,0) , (24,14) and (0,20)

But as  they want to offer both types of cookies this means that the case :

(0,0) ,(45,0) and (0,20) are discarded.

hence, we are left with the point (24,14)

Hence, the profit is:

z=24+1.50×14

z=$ 45

Hence, the maximum profit is: $ 45.

Hence, number of chocolate chip cookies=24 dozens.

As 1 dozen=12

Hence, 24 dozen=24×12=288 cookies.

Similarly Number of peanut butter cookies =14 dozen

Hence, 14 dozen=168 cookies.

g(x) is the negative form of f(x)? because whenever its the negative form it reflects its self over the x axis. idk if this is right though.

step-by-step explanation: