Hi Everyone, Below is my additional homework in Quantitative Analysis. I would l
ID: 445976 • Letter: H
Question
Hi Everyone,
Below is my additional homework in Quantitative Analysis. I would like to seek on your assistance in answering the below problem as well. Thank you.
Problem2:
A distributor buys a product from three plants and sells the product to seven customers. The profit he makes for each of product sold and the corresponding demand of each customer are as follows:
Customer
Profit per Unit ( in $)
Demand
North Plant
South Plant
West Plant
A
1.75
1.85
1.00
10
B
1.50
2.00
1.15
5
C
0.90
1.65
1.25
15
D
1.00
1.65
1.55
20
E
1.10
1.50
1.15
10
F
1.55
1.00
1.10
20
G
1.00
1.20
0.50
15
Total
95
The distributor used to have more than three sources of the products. But due to the depressed economy, his resources were reduced to only three plants with an aggregate supply of only 90 units as follows: 30 units from North Plant, 30 units from South Plant and another 30 units from West Plant. Furthermore, due to standardization, his customers are not willing to accept partial supply from any distributor, i.e., a customer will buy his total requirement from only one distributor. Determine which customer should he give up which would give the maximum profit based on a comparative analysis of the resulting profits for every customer given up?
Customer
Profit per Unit ( in $)
Demand
North Plant
South Plant
West Plant
A
1.75
1.85
1.00
10
B
1.50
2.00
1.15
5
C
0.90
1.65
1.25
15
D
1.00
1.65
1.55
20
E
1.10
1.50
1.15
10
F
1.55
1.00
1.10
20
G
1.00
1.20
0.50
15
Total
95
Explanation / Answer
Question is a typical transportation problem.
As mentioned in the question the total demand is 95 units but available supply is only 90 units , therefore a dummy plant is considered with balanced figure of 5 units
Solution to above transportation problem is as follows: MAXIMUM PROFIT =$137.75 with customer G left with 5 units
In other words optimal solution is as follows:
Customer Profit per Unit ( in $) Demand North Plant South Plant West Plant Dummy Plant A 1.75 1.85 1.00 0 10 B 1.50 2.00 1.15 0 5 C 0.90 1.65 1.25 0 15 D 1.00 1.65 1.55 0 20 E 1.10 1.50 1.15 0 10 F 1.55 1.00 1.10 0 20 G 1.00 1.2 0.50 0 15 Supply 30 30 30 5 95 / 95