Let the company manufacture x souvenirs of type A and y souvenirs of type
B. Therefore, x ≥ 0 and y ≥ 0
The given information can be complied in a table as follows.
The profit on type A souvenirs is Rs 5 and on type B souvenirs is Rs 6. Therefore, the constraints are
Total profit, Z = 5x + 6y
The mathematical formulation of the given problem
is Maximize Z = 5x + 6y … (1) subject to the
5x+8y≤ 200 .....(2)
5x+4y≤ 120 .....(3)
x, y ≥ 0 … (4)
The feasible region determined by the system of constraints is as follows.
The corner points are A (24, 0), B (8, 20), and C (0, 25).
The values of Z at these corner points are as follows.
The maximum value of Z is 200 at (8, 20).
Thus, 8 souvenirs of type A and 20 souvenirs of type B should be produced each day to get the maximum profit of Rs 160.