# Calculus

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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 - ,

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 - ,

are you sure its 17?

• Calculus - ,

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 - ,

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