A company decides to begin making and selling computers. The price function is given as follows: p=−50x+1900,

Question

where x is the number of computers that can be sold at a price of p dollars per unit. Additionally, the financial department has determined that the weekly fixed cost of production will be 7000 dollars with an additional cost of 150 dollars per unit.

(A) Find the revenue function in terms of x. R(x) =

(B) Use the financial department's estimates to determine the cost function in terms of x. C(x) =

(C) Find the profit function in terms of x. P(x) =

(D) Evaluate the marginal profit at x=250. P′(250) =

Answer 1

P =-50x + 1900

R= Px = -50x^2 + 1900x

C=7000+150x

Profit = R-C = -50x^2 +1750x -7000

Marginal Profit = (R-C)' = -100x + 1750

Marginal Profit when x=250, -100(250) + 1750 = a loss or negative profit = -23,250

Maximum profit is when Marginal profit = 0

-100x +1750 =0

100x = 1750

x = 17.5

Profit would then be -50(17.5)^2 + 1750(17.5) -7000 = $8,312.50