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The marginal revenue at the output level 4 is 24, marginal revenue at the output level 4 is 41, and marginal profit at the output level 4 is 17.
<h3>What is a marginal cost?</h3>
It is defined as the cost showing an increase in the cost when the number of units produced increases, In simple words it is the ratio of the cost to quantity.
We have a cost function of a product:
C(Q) = 3Q² +8
a) To find the marginal cost to differentiate it with respect to Q and plug
Q = 4:
C'(Q) = 6Q
C'(4) = 6(4) = 24
b) R(Q) = P×Q
R'(Q) = Q² - 20Q + 105
Plug Q = 4
R'(Q) = (4)² - 20(4) + 105
R'(Q) = 41
c) Marginal profit:
MP(Q) = R(Q) - C(Q)
After calculating:
MP'(Q) = Q² - 26Q + 105
Plug Q = 4
MP'(Q) = 16 - 104 + 105 = 17
Similar, we can find the maximum profit.
Thus, the marginal revenue at the output level 4 is 24, marginal revenue at the output level 4 is 41, and marginal profit at the output level 4 is 17.
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