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Question
Solve the following example: The total cost function of producing n notebooks is given by C= 1500 − 75n + 2n2 + `"n"^3/5`. Find the marginal cost at n = 10.
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Solution
Total cost function,
C = 1500 − 75n + 2n2 + `"n"^3/5`
Marginal Cost = `("dC")/("dn")`
=`"d"/("dn")(1500 - 75"n" + 2"n"^2 + "n"^3/5)`
=`d/(dn)(1500) - 75"d"/("dn")("n")+2"d"/("dn")("n"^2) + 1/5"d"/("dn")("n"^3)`
= `0 - 75(1) + 2(2"n")+1/5(3"n"^2)`
= `-75 + 4"n" + (3"n"^2)/5`
When n = 10,
Marginal cost
=`(("dC")/("dn"))_("n" = 10)`
= `-75 + 4(10) + 3/5 (10)^2`
= –75 + 40 + 60
= 25
∴ Marginal cost at n = 10 is 25.
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