Its a mathematical problem from operation management.

2. Quantity Discount with
constant carrying cost

3. Problem:
The 21000 seat Air east Arena houses
the local professional ice hockey,
basketball, indoor soccer and arena
football teams as well as various trade
shows wrestling and boxing matches,
tractor pulls and circuses. Arena
vending annually sells large quantities
of soft drinks and been in plastic cups
with the name of the arena. The local
container cup manufacturer that
supplies the cups in boxes of 100 has

4. offered arena management the
following discount price schedule for
cups.
The annual demand for cups is 2.3
million, the annual carrying cost per
box of cups is 1.90 and ordering cost
Order quantity (boxes) Price per box
2000-6999 47
7000-11999 43
12000-19999 41
20000 38

5. is 320 determine the optimal order
quantity and total annual inventory
cost.
Solution:
Given that,
D=
2.3∗1000000
100
=23000
k=320
h=1.9

6. EOQ= 2𝐾𝐷/ℎ
= 2 ∗ 2300 ∗ 320/1.9
=2783
TCU=
320∗2300
2783
+
2783∗1.9
2
+ (23000*47)
=1086289
TCU=
320∗23000
11999
+ 11999∗1.9
2
+ (2300*43)
=1001012

7. TCU=
320∗23000
19999
+
19999∗1.9
2
+ (23000*41)
=962367
TCU=
320∗23000
20000
+
20000∗1.9
2
+ (23000*38)
=893368
∴Total cost is 893368 and EOQ is 20000.