Problem 5.42

A particular product is manufactured in factories A, B, C and D; and is sold at centres 1, 2 and 3. The cost in Rs. of product per unit and capacity in kg per unit time of each plant is given below:

Factory Cost (Rs.) per unit Capacity (kg) per unit
A 12 100
B 15 20
C 11 60
D 13 80

The sale price in Rs. per unit and the demand in kg per unit time are as follows:

Sales centre Sale Price (Rs.) per unit Demand (kg) per unit
1 15 120
2 14 140
3 16 60

Required: Find the optimal sales distribution.


Step 1 → Formulating the given problem as a transportation problem. The profit matrix for various factories and sales counters is calculated below:

Step ...

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