Question

Suppose that it costs c(x) = 156.66x^2 + 13315.79x + 50600.00 dollars to produce (x) boats and that a price per unit of p(x) = -266.32x + 25300.00 is needed to sell all x units.

a.) Find the revenue function R(x) =

b.) Find the profit function P(x) =

c.) Find the exact cost on the 11th boat exact cost =

d.) Find the marginal profit if x=10

Marginal profit =

Answer 1

Cost function : c(x) = 156.66x² + 13315.79x + 50600.00

Price function : p(x) = -266.32x + 25300.00

(a) Revenue function : R(x) = x*p(x) => -266.32x² + 25300x

(b) P(x) => R(x) - C(x)

P(x) => (-266.32x² + 25300x) - (156.66x² + 13315.79x + 50600)

P(x) => - 422.98x² + 11984.21x - 50600

(c) c(x) = 156.66x² + 13315.79x + 50600

Exact cost of 11th boat => c(11) - c(10)

C(11) => 156.66*11² + 13315.79*11 + 50600 => 216029.55

C(10) => 156.66*10² + 13315.79*10 + 50600 => 199423.9

Exact Cost of producing 11th Unit : 16605.65

(d) Marginal Profit => P'(x) => - 845.96x + 11984.21

At x = 10,

P'(10) => - 845.96*10 + 11984.21

P'(10) => 3524.61