Question

HELP PLEASE!!!

These are the cost and revenue functions for a line of 24-pound bags of dog food sold by a large distributor:

R(x) = -31.72x2 + 2,030x
C(x) = -126.96x + 26,391

The maximum profit of $ ____ can be made when the selling price of the dog food is set to $ ____ per bag.

Answer 1

The maximum profit of $ 10277.32____ can be made when the selling price of the dog food is set to $ _34___ per bag.

Explanation:

Profit = Revenue - Cost

P(x) = R(x) -C(x)

= -31.72x^2 + 2,030x -( -126.96x + 26,391)

Distribute the minus sign

= -31.72x^2 + 2,030x+126.96x - 26,391

Combine like terms

= -31.72 x^2 + 2156.96 x - 26391

This is a parabola. It is facing downwards. The maximum profits is at the vertex ( where the max is)

vertex = h = -b/2a = -(2156.96)/(2*-31.72) = -2156.96/-63.44=34

Evaluate P(x) at x=34 to determine the profit

P(34) = -31.72 (34)^2 + 2156.96 (34) - 26391

-36668.32+73336.64-26391

10277.32