Question

A division of Chapman Corporation manufactures a pager. The weekly fixed cost for the division is $14,000, and the variable cost for producing x pagers/week in dollars is represented by the function V(x). $ V(x) = 0.000001x^3 - 0.01x^2 + 50x $ The company realizes a revenue in dollars from the sale of x pagers/week represented by the function R(x). $ R(x) = -0.02x^2 + 150x \; \quad \; (0 \leq x \leq 7500) $ (a) Find the total cost function C. What is the profit for the company if 2,600 units are produced and sold each week?

Answer 1

Answer:

P=$-303,424

Step-by-step explanation:

given data

fixed cost= $14,000

variable cost function

$V(x) = 0.000001x^3 - 0.01x^2 + 50x$

revenue function

$R(x) = -0.02x^2 + 150x \; \quad \; (0 \leq x \leq 7500)$

a. we know that total cost C=fixed cost plus variable cost

C=14000+0.000001x^3 - 0.01x^2 + 50x

$C=14000+0.000001x^3 - 0.01x^2 + 50x$

profit is given as revenue minus the total cost

P=R(x)-C   (x=2600)

$P=-0.02x^2 + 150x -(14000+0.000001x^3 - 0.01x^2 + 50x)$

substitute x=2600

$P=-0.02(2600)^2 + 150(2600) -(14000+0.000001(2600)^3 - 0.01(2600)^2 + 50(2600))$

$P=-135200+390000-(1400+17576-67600)$

$P=-254800-(48624)\\\\P=-254800-48624\\\\P=-303,424$