A manufacturer determines that the demand function for the parts is
$p = \frac{1500}{\sqrt{x}}$
where x is the demand for the products at a given price, p. The cost of producing x parts
is given by the following cost function:
$C(x) = 15x + 150\sqrt{x} + 12,500$
Determine the marginal cost, marginal revenue, and marginal profit at x = 100 parts.
1. Determine the cost of the product line when x = 100 parts.
2. Marginal cost is the derivative of the cost function, so take the derivative and evaluate it
at x = 100.
Thus, the marginal cost at x = 100 is $
producing the 101st part.
this is the approximate cost of
Revenue, R(x), equals the number of items sold, x, times the price, p:
$R(x) = xp$
3. Determine the total revenue when 100 parts are sold.
Marginal revenue is the derivative of the revenue function, so take the derivative of R(x)
and evaluate it at x = 100:
Thus, the approximate revenue from selling the 101st part is $
