Answer is not 122736X Terry makes and sells necklaces He has

Answer is not 12(27)-36X

Terry makes and sells necklaces. He has observed over time that when the price is $12 each, he sells an average of 27 per day. If he increases the price, then his average sales fall by 3 per day for each dollar increase. The materials for each necklace cost $5. Express his profit P as a function of x, the number of necklaces sold. Answer: P(x)= 27x - 3x^2

Solution

Price = $12

Let no. of necklaces sold be x

$12 ---- 27 per day

$13 ---- 24 per day

Demand curve : at price z, demand, x = 27 -3(z -12)

x = 27 -3z +36

x = 63 -3z

(price) z= 21 -x/3

sales = x*z = 21x -x^2/3

Cost = 5x

So, Profit function = sales -cost = -x^2/3 +21x -5x = -x^2/3 +17x