Homework Help: Calculus

Posted by Casey on Saturday, March 3, 2012 at 2:48pm.

A sporting goods store sells 100 pool tables per year. It costs $20 to store one pool table for a year, based on the average inventory on hand. It costs $40 for each delivery of pool tables. How many times per year and in what lot size should the store order pool tables to minimize its inventory costs?

I am confused for this one.

Calculus - Susan, Saturday, March 3, 2012 at 3:27pm
I'm not sure but I'll explain my thinking:
t= # of deliveries
p = # of tables in each delivery
40t+20p = Inventory costs
tp=100 because 100 are sold a year, t=100/p
40(100/p)+20p = Inventory costs
4000/p + 20p = Inventory costs
To minimize set derivative = 0
-4000/p^2 +20=0
p = sqrt 200=
about 17 pool tables, 100/17 = 6 times a year
Calculus - Casey, Saturday, March 3, 2012 at 4:19pm
are you sure its 17?
Calculus - Susan, Saturday, March 3, 2012 at 4:49pm
No! I am mistaken the square root of 200 is approximately 14 = p
100/14=# of times
7 gives you 98 tables
8 deliveries gives you 112

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