Answer:
a) $109
b) [tex]P(q) = \frac{45q}{ln(q)} +90[/tex]
c) [tex]$11.20[/tex]
Step-by-step explanation:
a) The marginal cost, or the cost per additional unit, is given by the derivate of the cost function:
[tex]C(q) = 109q+90\\C(q) = \$109[/tex]
b) Profit is given by Revenue minus Cost:
[tex]P(q) = R(q) - C(q)\\P(q) = \frac{45q}{ln(q)} +90[/tex]
c) The marginal profit for 8 units, is given by the difference in profit for 9 units and 8 units:
[tex]M = P(9)-P(8)\\M= \frac{45*9}{ln(q)} +90 - (\frac{45*8}{ln(8)}+90 )\\M=\$11.20[/tex]
By applying the basic formulae,
a) $109
b)[tex]P(q) = \frac{45q}{lnq} - 90[/tex]
c) $11.20
Marginal cost is a derivative of the Cost function.
a)Marginal cost
C(q) = 109q + 90
[tex]M(q) = \frac{d}{dq} C(Q)=\frac{d}{dq} ( 109q+90)\\\\M(q) = 109$[/tex]
Marginal cost = $109
(b)Profit function P(q) = Revenue function R(q) - Cost function C(q)
[tex]P(q) = (109q + \frac{45q}{ln q}) - (109q +90) = \frac{45q}{lnq} -90[/tex]
(c) Marginal profit = P(9)-P(8)
Marginal profit [tex]= \frac{45*9}{ln9} - \frac{45*8}{ln8}= 11.20[/tex]
Thus we find Marginal cost, Profit function, and Marginal profit as,
a) $109
b) [tex]P(q) = \frac{45q}{lnq} - 90[/tex]
c) $11.20
To get more about cost function, revenue function, profit function, etc. refer to the link,
https://brainly.com/question/2292799
