SOLUTION: Total profit P is the difference between total revenue R and total cost C. Given the following​ total-revenue and​ total-cost functions, find the total​ profit, t
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Question 1058413: Total profit P is the difference between total revenue R and total cost C. Given the following total-revenue and total-cost functions, find the total profit, the maximum value of the total profit, and the value of x at which it occurs.
R(x)= 1000x-(x squared)
C(x)= 3400+10x
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Total profit P is the difference between total revenue R and total cost C.
Given the following total-revenue and total-cost functions, find the total profit, the maximum value of the total profit, and the value of x at which it occurs.
R(x)= 1000x-x^2
C(x)= 3400+10x
:
Profit = Revenue - Cost
P(x) = (1000x - x^2) - (3400+ 10x)
remove brackets
P(x) = 1000x - x^2 - 3400 - 10x
combine like terms
P(x) = -x^2 + 1000x - 10x - 3400
A quadratic equation
P(x) = -x^2 + 990x - 3400
Max profit occurs on the axis of symmetry, x = -b/(2a)
x =
x = 495 units will produce max profit
Find that actual profit
P(x) = -(495^2) + 990(495) - 3400
P(x) = -245025 + 490050 - 3400
P(x) = $241,625 value of the total profit
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