40 3x + 4x = -15 5x, + 4x, s 200 20 (400 13 13 30 3x, *.43 3x, 5x, S 150 0 = 0 x +4, 2806 5x + 4x2 100 08 -4K 20 30 40 50 f24 B, Fig. 2.6 Any point in the shaded region is a feasible solution to the given problem. The co-ordinates of the vertices of this convex region ABCDE are 400 150 A(20, 0), B(0, 25), C(O, 30), D and E(40, 0). 1313 Values of the objective function Z = 3x + 4x, at these vertices are 1,800 Z(A) = 60, ZB) = 100, Z(C) = 120, Z(D) = Z(E) = 120 13 1,800 400 150 Since the maximum value of Z is which occurs at the vertex D the 13 13 13 solution to the given problem is 400 150 1,800 X x = and Zmax 138.46. 13 13 13 EXAMPLE 2.9-5 Mohan-Meakins Breveries Ltd. has two bottling plants, one located at Solan and the other at Mohan Nagar. Each plant produces three drinks, whisky, beer and fruit juices named A, B and C respectively. The number of bottles produced per day are as follows: Plant ar Solan Mohan Nagar (S) (M) Whisky, A 1,500 Beer, B 3.000 1.000 Fruit juices, C 2,000 5.000 A market survey indicates that during the month of April there will be a demand of 20.000 1.500