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.

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

Step-by-step 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

Max profit is: $10,277.32

Selling price: $951.52

Step-by-step explanation:

Profit = Revenue - Cost

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

Profit = -31.72x² + 2156.96x - 26391

= -31.72(x² - 68x + 34² - 34²) - 26391

= -31.72(x² - 2(34)(x) + 34²) + 31.72(34²) - 26391

= -31.72(x - 34)² + 10277.32

Max profit is: $10,277.32

When x = 34

Revenue = -31.72(34²) + 2030(34)

= 32351.68 for 34 bags

Per bag:

32351.68/34

$951.52

10 * 563.67 = 5636.7

one that is bigger than 3 1/2