Posted by Casey on .
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,
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,
are you sure its 17?

Calculus 
Susan,
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 
Calculus 
Fares,
A sporting goods store sells 140 pool tables per year. It costs $50 to store one pool table for a year. To reorder, there is a fixed cost of $35 per shipment plus $12 for each pool table. How many times per year should the store order pool tables, and in what lot size, in order to minimize inventory costs
The store should order
nothing pool tables
the store should order() then () times per year to minimize inventory costs