SOLUTION: Find the maximum profit if the revenue and cost functions are given by the following equations: R = 220x

Click here to see ALL problems on Miscellaneous Word Problems

Question 1111167: Find the maximum profit if the revenue and cost functions are given by the following equations:
R = 220x - x2 and C = 70x +2300.
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
Find the maximum profit if the revenue and cost functions are given by the following equations:
R = 220x - x^2 and C = 70x +2300.
Profit - revenue - cost
P(x) = (220x - x^2) - (70x+2300)
Remove the brackets and arrange as a quadratic equation
P(x) = 220x - x^2 - 70x - 2300
P(x) = -x^2 + 150x - 2300
Max profit occurs at the axis of symmetry; x = -b/(2a)
x =
x = 75 units sold give max profit, substitute 75 for x in the equation
P(x) = -(75^2) + 150(75) - 2300
P(x) = - 5625 + 11250 - 2300
P(x) = $3325 is max profit (75 units are sold)

SOLUTION: Find the maximum profit if the revenue and cost functions are given by the following equations: R = 220x - x2 and C = 70x +2300.