Question

During the summer months terry makes necklaces to sell on the beach. Last summer he sold necklaces for 10 dollars each and averaged 20 sales per day. When he increased the price by 1 dollar he found that he lost 2 sales per day. If the material for each necklace costs Terry 6 dollars what should the selling prices be to maximize his profit? Profit=Revenue-Cost

Answer 1

10 dollars * 20 sales = 200 dollars, cost= 6 * 20 = 120, Total profits = 200-120=80d
or
11 dollars * 18 sales = 198 dollars, cost = 6 * 18 = 108, Toal profits = 198-108=90d

So, you can see that when terry increases his price by one dollar he makes an extra 10 dollars per day, even though on average he loses two customers.

Answer 2

Demand function with slope -1/2 and the given point ( 20, 10 )
y -10 = ( -1/2 ) ( x - 20 )
-> y = -.5x + 20

Profit function P(x):
P(x) = ( -.5x + 20 - 6 ) x
= - .5x² + 14x
Maximize Profit:
P'(x) = 0 .... --> x = ... ==> y = ....