Business Calculus Minimize Inv Cost

  • Thread starter KevinJay
  • Start date
  • #1
1
0

Homework Statement


A sporting goods store sells 135 pool tables per year. It costs $10 to store one pool table for a year. To reorder, there is a fixed cost of $27 per shipment plus $18 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?[/B]


Homework Equations


Yearly Carrying Cost = $10 (x/2) -> 5x
Yearly Reorder Cost = 27+18x(135/x)

The Attempt at a Solution


C(x) = 5x + (45x) (135/x)

Am I doing this right? I can't tell since I messed up when I was taking my notes... Im not sure how to continue. I know I have to find the derivative after, but I don't know how I would condense X
 

Answers and Replies

  • #2
35,120
6,860

Homework Statement


A sporting goods store sells 135 pool tables per year. It costs $10 to store one pool table for a year. To reorder, there is a fixed cost of $27 per shipment plus $18 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?[/B]


Homework Equations


Yearly Carrying Cost = $10 (x/2) -> 5x
Yearly Reorder Cost = 27+18x(135/x)
It's always a good idea to explicitly state what any variable represents. For this problem 'x' could be the number of pool tables to order in a shipment, or it could be the number of times per year to reorder.
KevinJay said:

The Attempt at a Solution


C(x) = 5x + (45x) (135/x)

Am I doing this right? I can't tell since I messed up when I was taking my notes... Im not sure how to continue. I know I have to find the derivative after, but I don't know how I would condense X
 
  • #3
Ray Vickson
Science Advisor
Homework Helper
Dearly Missed
10,706
1,722

Homework Statement


A sporting goods store sells 135 pool tables per year. It costs $10 to store one pool table for a year. To reorder, there is a fixed cost of $27 per shipment plus $18 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?[/B]


Homework Equations


Yearly Carrying Cost = $10 (x/2) -> 5x
Yearly Reorder Cost = 27+18x(135/x)

The Attempt at a Solution


C(x) = 5x + (45x) (135/x)

Am I doing this right? I can't tell since I messed up when I was taking my notes... Im not sure how to continue. I know I have to find the derivative after, but I don't know how I would condense X

This is a standard Economic Order Quantity (EOQ) model, as found in any Operations Research textbook, or on-line; see, eg.,
https://en.wikipedia.org/wiki/Economic_order_quantity .
 

Related Threads on Business Calculus Minimize Inv Cost

Replies
1
Views
10K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
1
Views
10K
  • Last Post
Replies
3
Views
6K
Replies
15
Views
6K
Replies
0
Views
2K
Replies
2
Views
2K
  • Last Post
Replies
5
Views
4K
  • Last Post
Replies
18
Views
838
  • Last Post
Replies
0
Views
2K
Top