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
Algebra.Com
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.
RELATED QUESTIONS
Total profit P is the difference between total revenue R and total cost C. Given the... (answered by solve_for_x)
Total profit P is the difference between total revenue R and total cost C. Given the... (answered by ankor@dixie-net.com)
Maximizing profits: In business, profit is the difference between revenue and cost; that... (answered by lwsshak3)
A farmer decides to enclose a rectangular garden, using the side of a barn as one... (answered by ikleyn,josmiceli)
Total profit P is the difference between total revenue R and total cost C. Given the... (answered by ikleyn)
Recall that total profit P is the difference between total revenue R and total cost C.... (answered by nerdybill)
The total profit is defined as total revenue, R(x), minus total cost C(x), and is given... (answered by Aldorozos)
a company produces x units of a product per month, where C(x) represents the total cost... (answered by LinnW)
The total profit is defined as total revenue, R(x), minus total cost C(x), and is given... (answered by josgarithmetic)