Correct question is;
A manufacturer determines that the number of drills it can sell is given by the formula,D = -4p2 + 160p – 305 where p is the price of the drills in dollars.
A) At what price will the manufacturer sell the maximum number of drills?
B) What is the maximum number if drills that can be sold?
Answer:
A) $20
B) D_max = 1295 drills
Step-by-step explanation:
We are given that the price for number of drills it can sell is given by the formula, D = -4p² + 160p – 305 where p is the price of the drills in dollars.
A) To find the price for selling maximum number of drills, we will find the derivative of the function D and equate to zero.
D' = -8p + 160
Equating to zero gives;
-8p + 160 = 0
8p = 160
p = 160/8
p = $20
B) maximum number of drills will occur at p = $20.
Thus;
D_max = -4(20)² + 160(20) – 305
D_max = -1600 + 3200 - 305
D_max = 1295
