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, the maximum v
Question 1157181: 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.
Upper R left parenthesis x right parenthesis equals 1200 x minus x squared
R(x)=1200x−x2,
Upper C left parenthesis x right parenthesis equals 3000 plus 20 x
C(x)=3000+20x Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! r(x) = 1200x - x^2
c(x) = 3000 + 20x
p(x) = r(x) - c(x)
that becomes:
p(x) = 1200x - x^2 - (3000 + 20x)
simplify to get:
p(x) = 1200x - x^2 - 3000 - 20x
combine like terms to get:
p(x) = -3000 + 1180x - x^2
order the terms in descending order of degree to get:
p(x) = -x^2 + 1180x - 3000
a = the coefficient of the x^2 term = -1
b = the coefficient of the x term = 1180
c = the constant term = -3000
the maxim profit is when x = -b/2a.
that becomes x = -1180/-2 = 590.
the maximum profit is the value of the equation at x = 590
that becomes p(x) = 345,100
that's your solution.
here's the graph that confirms that.
