Answer:
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
Answer:
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
