Question
During the Christmas season a promotional company purchases cheap red felt stockings, glues fake white fur and sequins onto them and packages them for distribution.
The total cost of producing q cases of stockings is given by
c = 3q^2 + 50q − 18qlnq + 120
Find the number of cases that should be processed in order to minimize the average cost per case. Determine (to two decimal places) this minimum average cost.
The total cost of producing q cases of stockings is given by
c = 3q^2 + 50q − 18qlnq + 120
Find the number of cases that should be processed in order to minimize the average cost per case. Determine (to two decimal places) this minimum average cost.
Answers
oobleck
average cost is a(q) = c(q)/q = 3q + 50 - 18lnq + 120/q
da/dq = 3 - 18/q - 120/q^2
da/dq = 0 at q=10, so a(10) = 92-18ln10
a" > 0 so that is a minimum
da/dq = 3 - 18/q - 120/q^2
da/dq = 0 at q=10, so a(10) = 92-18ln10
a" > 0 so that is a minimum