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dybincka [34]
3 years ago
15

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)equa

ls109 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.
Mathematics
1 answer:
Tcecarenko [31]3 years ago
6 0

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

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