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2 answers:
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Answer:
(a)$13
(b) Loss of $4
Step-by-step explanation:
C(q) represents Cost of producing q units.
R(q) represents Revenue generated from q units.
P(q) represents Total Profit made from producing q units.
Marginal analysis is concerned with estimating the effect on quantities such as cost, revenue, and profit when the level of production is changed by a unit amount. For example, if C(q) is the cost of producing q units of a certain commodity, then the marginal cost, MC(q), is the additional cost of producing one more unit and is given by the difference
MC(q) = C(q + 1) − C(q).
Using the estimation
C'(q)≈=C(q+1)-C(q)
We find out that MC(q)=C'(q)
We can therefore compute the marginal cost by the derivative C'(q).
This also holds for Revenue, R(q) and Profit, P(q).
(a) If C'(50)=75 and R'(50)=88
51st item.
P'(50)=R'(50)-C'(50)
=88-75=$13
The profit earned from the 51st item will be approximately $13.
(b) If C'(90)=71 and R'(90)=67, approximately how much profit is earned by the 91st item.
P'(90)=R'(90)-C'(90)
=67-71= -$4
The profit earned from the 91 st item will be approximately -$4.
There was a loss of $4.