How much should each cup of lemonade be sold for in order to maximize the profit? (e)

Question

Economics At the New York State Fair, it costs $500 to rent a 5-foot booth for a lemonade stand, and it costs an average of $1 in material and labor to make each cup of lemonade. When the booth sells each cup of lemonade for $4, they sell 100 cups. When the price is decreased to $3.50, they sell 30 more cups.

(a) Find the cost function

C= 500+x

b.) Find the price function, assuming it is linear (p = mx + b)

p= -1/60x +17/3

c.) Find the revenue function.

- R= 1/60x^2 +17/3x

(d) Find the Profit function.

-1/60x^2 +14/3x -500

(e) How much should each cup of lemonade be sold for in order to maximize the profit?

????????????????

Answer 1