Homework SourseBon Temps Surf and SCUBA Shop sells 360 surfboards per year
Bon Temps Surf and SCUBA Shop sells 360 surfboards per year. It costs $8 to store one surfboard for a year. Each reorder costs $10, plus an additional $5 for each surfboard ordered. a) Find the total cost function. b) How many times per year should the store order surfboards, and in what lot size, in order to minimize inventory cost? c) What would be the minimum and maximum costs?
Solution
sol: suppose that, TC = 100 + 10Q + 20Q^2 ATC=TC/Q = 100/Q + 10Q/Q + 20Q2/Q= = 100/Q + 10 + 20Q Cost function A) MC=(TC)\'=(100 + 10Q + 20Q^2)\'= =10+2*20*Q=10+40Q ___________ MC(Q=10)=10+40*10=10+400=410 ___________ Cost function B) ATC(min)->(ATC)\'=0 (100/Q + 10 + 20Q)\'=0 -100/(Q^2)+20=0 20=100/(Q^2) 20*Q^2=100 Q^2=100/20=5 ___________ Q=Sqrt(5)=2.236 ___________ Cost function C) ATC=MC 100/Q + 10 + 20Q=10+40Q 100/Q=20Q 20*Q^2=100 Q^2=5 ___________ Q=Sqrt(5)=2.236
