I got the Cx 10x9000 The Professor said this to me The cost

I got the C(x)= 10x+9000

(The Professor said this to me) The cost function is fine. Use the break even points – 30 items, and 100 items to find a profit function. The use the profit and cost functions to find the revenue function. (PLEASE SOMEONE HELP)

Solution

C(x)= 10x+9000

Let price function be be p(x) = ax +b

Revenue function : R(x) = x(ax +b)

At breakeven points : x = 30 ; R(x) = C(x)

x(ax +b) = 10x +9000

900a + 30b = 9300 ----(1)

10000a + 100b = 10,000 -----(2)

Solve the equations 1 and 2 we get :

p(x) = -3x + 400

R(x) = x(-3x +400) = -3x^2 + 400x