SOLUTION: I worked this math problem but it says I am wrong, what did I do and what is the correct answer? Rite-Cut riding lawnmowers obey the demand equation p= -1/20x+1,030. The cost of p

Question 918925: I worked this math problem but it says I am wrong, what did I do and what is the correct answer?
Rite-Cut riding lawnmowers obey the demand equation p= -1/20x+1,030. The cost of producing x lawnmowers is given by the function C(x)= 150x+3,000.
Express the profit p as a function of x. Simplify but do not factor answer.
I got the answer -1/20x^2+880x-3,000

Found 2 solutions by ewatrrr, rothauserc:
Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!
demand = p = -1/20x+1,030.
R(x) = px = (-1/20)x^2 + 1030x
P(x) = R(x) - C(x)
P(x) = (-1/20)x^2 + 1030x - (150x + 3000)
P(x) = (-1/20)x^2 + 880x - 3000
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
in demand equation p = -1/20x+ 1,030, p is the price x units can be sold
cost of producing x lawnmowers is C(x)= 150x+3,000
profit p = (x * price x units can be sold) - cost of producing x lawnmowers
profit p = (x * (-1/20x + 1,030)) - (150x + 3,000)
profit p = -1/20x^2 + 1030x - 150x -3000
profit p = -1/20x^2 + 880x - 3000
I think your answer is correct
In order to find the max profit, we need to calculate the vertex of the profit parabola - note that the parabola opens downward.
x coordinate = -b/2a = -880 / (2*(-1/20)) = 880 / (1/10) = 8800
substitute for x in the profit equation
max profit = (-1/20)*8800^2 + (880*8800) - 3000
max profit = 3,869,000

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