A division of Chapman Corporation manufactures a pager. The weekly fixed cost for the division is $10,000, and the variable cost for producing x pagers/week in dollars is represented by the function V

(a) To find the total cost function C, we add the weekly fixed cost of $10,000 to the variable cost function V(x): {eq}begin{aligned} C(x) &= 10,000 + V(x) \ &= 10,000 + (0.000001x^3 - 0.01x^2 + 50x) end{aligned} {/eq} (b) To find the total profit function P, we subtract the total cost function C from the revenue function R: {eq}begin{aligned} P(x) &= R(x) - C(x) \ &= (-0.02x^2 + 150x) - (10,000 + 0.000001x^3 - 0.01x^2 + 50x) \ &= -0.000001x^3 + 0.01x^2 + 100x - 10,000 end{aligned} {/eq} (c) To find the profit for the company if 1,700 units are produced and sold each week, we substitute x = 1,700 into the profit function: {eq}begin{aligned} P(1,700) &= -0.000001(1,700)^3 + 0.01(1,700)^2 + 100(1,700) - 10,000 \ &= 357,200 end{aligned} {/eq} Therefore, the profit for the company if 1,700 units are produced and sold each week is $357,200.