Algebra-Economics word problem

Question

Suppose a company has fixed costs of $35,200 and variable cost per unit of
2/5x + 333 dollars, where x is the total number of units produced. Suppose further that the selling price of its product is
1465 − 3/5x dollars per unit.

 

(a) Find the break-even points. (Enter your answers as a comma-separated list.)
x =


(b) Find the maximum revenue. (Round your answer to the nearest cent.)
$


(c) Form the profit function P(x) from the cost and revenue functions.
P(x) =


Find maximum profit.
$

(d) What price will maximize the profit? (Round your answer to the nearest cent.)

 

I keep getting the wrong answers for all of this. 

Answer 1

breakeven points are when Revenue = Cost

Revenue = px = 1465x - 3x^2/5

cost = 35200+ 2x/5 + 333x

R=C when 1465x - 3x^2/5 = 35200 +2x/5 + 333x

graph and find where they intersect

x = about 1854 and 32

or convert to a quadratic

factor, complete the square, use the quadratic formula or graph the equation and find the x intercepts

for maximum revenue, 1465 -6x/5 = 0

x = 5(1465)/6 = about 1221

Profit function = P(x) = R(x) -C(x)= 1465x -.6x^2- 35200 - 2x/5 -333x

profit maximizing output x is when

P' = 0 = 1465 -12x -.4 -333

12x = 1132 -.4 = 1131.6

x = 1131.6/12 = 94.3

profit maximum = 1465(94.3) -6(94.3^2) -35200 -2(94.3)/5 -333(94.3)

profit maximizing price is = 1465 - .6(94.3) =$1,408.42