A company plans to start manufacturing three new products. It owns five plants t
ID: 353347 • Letter: A
Question
A company plans to start manufacturing three new products. It owns five plants three of which are to be selected to produce the three new products. The follow ing tables give the estimated production costs and distribution costs per unit of each product ifit were manufactured at each plant Unit Production Costs (S) Product 10 15 20 20 20 Unit Distribution Costs (S) Piant 10 30 50 15 30 Plans call for the following annual production of each product to be sold at the following prices Planned Planned Price (S) Product 3,000 5,000 10 Formulate this problem as an assignment problem to maximize total proft Find the solution and the profit associated with itExplanation / Answer
Problem requires to maximize the profit so the cost should be minimized .Since there is no variability associated with cost , so we can add both cost of production and distribution cost per unit to calculate total cost.
Total Cost = production cost + distribution cost
So Total Cost Matrix :
Plant
Product
1
2
3
4
5
1
20
45
30
10
25
2
7
70
6
35
50
3
4
6
3
8
8
Using the Assignment method , subtract the smallest number in each row from itself and all other numbers in the row.
Plant
Product
1
2
3
4
5
1
10
35
20
0
15
2
1
64
0
29
44
3
1
3
0
5
5
Subtract the smallest number in each column from itself and all other numbers in the column.
Plant
Product
1
2
3
4
5
1
9
32
20
0
10
2
0
63
0
29
39
3
0
0
0
5
0
Applying Line test , we can cover all the zeroes using 3 lines ,so optimal solution is:
Plant
Product
1
2
3
4
5
1
9
32
20
0
10
2
0
63
0
29
39
3
0
0
0
5
0
So Optimal product assignment to plant and its cost:
Product
Plant
Cost
1
4
10
2
3
6
3
1
4
Profit for all 3 products will be :
Product
Production
Price
Cost
Profit
1
3000
13
10
9000
2
15000
10
6
60000
3
2000
4
4
0
Total Profit
69000
Plant
Product
1
2
3
4
5
1
20
45
30
10
25
2
7
70
6
35
50
3
4
6
3
8
8
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