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Question
Solve the following example: The total cost of ‘t’ toy cars is given by C=5(2t)+17. Find the marginal cost and average cost at t = 3.
Solution
Total cost of ‘t’ toy cars, C = 5(2t) + 17
Marginal Cost =`("dC")/"dt"`
= `d/dt [5(2^t) + 17]`
=`5"d"/"dt"(2^"t")+"d"/"dt"(17)`
= 5(2t . log 2) + 0
= 5(2t . log 2)
When t = 3,
Marginal cost =` (("dC")/("dt"))_("t" = 3)`
= 5(23. log 2)
= 40 log 2
Average cost =`"C"/"t"= (5(2)^"t"+17)/t`
When t = 3, averagecos = `(5(2^3) + 17)/3`
= `(40+ 17)/3` = 19
∴ at t = 3, Marginal cost is 40 log 2 and Average cost is 19.
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