(i) Let x be the number of balls of type A and y be the number of balls of type B. Then Maximise profit is Z = 3x + 5y
(ii) Balls constraints 2x + y < 2000 investment constraint x + y < 1500 Therefore; Maximise; Z = 3x + 5y, 2x + y < 2000, x + y < 1500, x < 0, y < 0
(iii) In the figure the shaded region OABC is the fesible region. Here the region ¡s bounded. The corner points are O(0, 0), A(1000, 0) B(500, 1000), C(0, 1500). Given; Z = 3x + 5y
Corner points |
Value of Z |
O |
Z = 3(0)+ 5(0) = 0 |
A |
Z = 3(1000) + 5(0) = 3000 |
B |
Z= 3(500) + 5(1000) = 6500 |
C |
Z= 3(0) + 5(1500) = 7500 |
Since maximum value of Z occurs at C, the solution is
Z = 3(0) + 5(1500) = 7500.