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.
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
are you sure its 17?
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
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
To determine the optimal order quantity and frequency of pool tables, we need to find the Economic Order Quantity (EOQ). The formula for EOQ is:
EOQ = √(2DS/H)
Where:
D = Annual demand (number of pool tables sold per year)
S = Cost per order (delivery cost)
H = Holding cost per unit per year (storage cost)
Let's calculate each variable:
D = 100 pool tables per year (given)
S = $40 for each delivery (given)
H = $20 to store one pool table for a year (given)
Substituting these values into the EOQ formula:
EOQ = √(2 * 100 * 40 / 20)
Simplifying:
EOQ = √(8000 / 20)
EOQ = √400
EOQ = 20
The EOQ is 20 pool tables. This means that the store should order 20 pool tables per order. Now, to determine the optimal order frequency, we divide the annual demand (D) by the EOQ:
Order frequency = D / EOQ
Order frequency = 100 / 20
Order frequency = 5
The store should order pool tables 5 times per year with an order quantity of 20 pool tables each time to minimize its inventory costs.