Panchtantra Case

a) Decision Variables L = Lungis Production ( in metres ). S = Lungis Production ( in metres ).

b) Objective Function Maximise(0.9L + 0.6S ) 0.9L + 0.6S = Z

c) Constraints 0.2L + 0.0833S <= 3000 ( No of loom days constraints ) ----------------------------- (1) 0.04L <=480 ( 60’s Yarn weight constraint ) ----------------------------- (2) 0.06L +0.1S <= 2400 ( 40’s Yarn weight constraint ) ----------------------------- (3) L < = 11000 ( Lungi sales constraint in meters ) ----------------------------- (4) S <= 22000 ( Shirts sales constraint in meters ) ----------------------------- (5)

Question 1 Ganesh’s Idea of maximizing Lungis L = 11000 Substituting L in - (1) to get S S = 9600
Putting L and S in (3) to verify the constraints 11000 X.06 + 9600 X .1 <=2400 ------- Satisfied. Putting these values in objective function to get Ganesh’s Profit 0.9 X 11000 + 0.6 X 9600 = 15660

Objective Function Value using the optimum solution.

L= 6666.67 S= 20000 0.9 X 6666.67+ 0.6 X 20000 = 18000

Hence, we can conclude that Ganesh’s idea of maximizing profit by just increasing lungis is not better than the proposal of Mr Ganapathy

Question 2

Ganesh wants to ensure that minimum wages should be 20.50 per loom day
So this introduces and additional constraint for the wages

(4.5L /3000) + (1.5S /3000) >= 20.50

Upon Solving the