IELM 202, Assignment #2 Solution
Due date: 5 October 2005, Wednesday, 12:00 noon
Question 1 (25 marks):
A company has two manufacturing plants (
A
and
B
) and three sales outlets (
I
,
II
,
III
).
Shipping costs from the plants to the outlets in $/unit are as follows:
Outlet
Plant
I
II
III
A
4
6
8
B
7
4
3
The company wants to plan production, shipping and sales for the next two periods. The
manufacturing and demand data for the two periods are shown in the following tables. The
plants can store products produced in one period for sale in the next. The maximum storage
at each plant is 50 units and the inventory cost is $1 per unit. Formulate the problem as Liner
Programming to maximize the company profit.
Manufacturing Data
Plant A
Plants B
Period
Unit cost ($/unit)
Capacity
Unit cost ($/unit)
Capacity
1
8
175
7
200
2
10
150
8
170
Demand Data
Selling price ($/unit)
Maximum sales
Period
I
II
III
I
II
III
1
15
20
14
100
200
150
2
18
17
21
150
300
150
VARIABLE DEFINITIONS
P
A-1
, P
B-1
, P
A-2
, P
B-2
: production at A and B in the two periods
S
I-1
, S
II-1
, S
III-1
: sales in period 1 at three locations
S
I-2
, S
II-2
, S
III-2
: sales in period 2 at three locations
x
A-I-1
, x
A-II-1
, x
A-III-1
, x
B-I-1
, x
B-II-1
, x
B-III-1
: shipments in period 1
x
A-I-2
, x
A-II-2
, x
A-III-2
, x
B-I-2
, x
B-II-2
, x
B-III-2
: shipments in period 2
I
A
, I
B
: Inventory storage at A and B