Calculus

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.

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  1. 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

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  2. are you sure its 17?

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  3. 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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  4. 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

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