Question

The cost function for q units of a certain item is ​C(q)equals109 q plus 90. The revenue function for the same item is ​R(q)equals109 q plus StartFraction 45 q Over ln q EndFraction . a. Find the marginal cost. b. Find the profit function. c. Find the profit from one more unit sold when 8 units are sold.

Answer 1

Answer:

a) $109

b) $P(q) = \frac{45q}{ln(q)} +90$

c) $11.20$

Step-by-step explanation:

a) The marginal cost, or the cost per additional unit, is given by the derivate of the cost function:

$C(q) = 109q+90\\C(q) = \ 109$

b) Profit is given by Revenue minus Cost:

$P(q) = R(q) - C(q)\\P(q) = \frac{45q}{ln(q)} +90$

c) The marginal profit for 8 units, is given by the difference in profit for 9 units and 8 units:

$M = P(9)-P(8)\\M= \frac{45*9}{ln(q)} +90 - (\frac{45*8}{ln(8)}+90 )\\M=\ 11.20$