CASE STUDY CHALLENGE

Linear Programming: Transportation Problem

There are two factories located one at P and the other at Q. From these locations, a certain commodity is to be delivered to each of the three depots situated at A, B, and C.

  • • Requirements: Depot A (4 units), Depot B (4 units), Depot C (6 units).
  • • Production Capacity: Factory P (9 units), Factory Q (5 units).

Cost of Transportation (in ₹ per unit):

From / To A B C
P 160 100 150
Q 100 120 100

Transportation Network Diagram

 

Let \( x \) units and \( y \) units of the commodity be transported from factory P to the depots at A and B respectively.

Answer the following:

(i) Find (in terms of \( x \) and \( y \)) how many units of commodity be transported from factory P to depot C.
(ii) Find how many units of commodity be transported from factory Q to A, B, and C respectively.
(iii)

(a) Using (i) and (ii), find the total transportation cost \( Z \).

— OR —

(b) Using (i) and (ii), find the constraint inequalities for minimum cost \( Z \).
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