Question -
Answer -
Let the company manufacture x souvenirs of type A and ysouvenirs of type B respectively
Hence,
x ≥ 0 and y ≥ 0
The given information can be compiled in a table is given below
| Type A | Type B | Availability |
| Cutting (min) | 5 | 8 | 3 × 60 + 20 = 200 |
| Assembling (min) | 10 | 8 | 4 × 60 = 240 |
The profit on type A souvenirs is Rs 5 and on type B souvenirsis Rs 6. Hence, the constraints are
5x + 8y ≤ 200
10x + 8y ≤ 240 i.e.,
5x + 4y ≤ 120
Total profit, Z = 5x + 6y
The mathematical formulation of the given problem can be writtenas
Maximize Z = 5x + 6y …………… (i)
Subject to the constraints,
5x + 8y ≤ 200 ……………. (ii)
5x + 4y ≤ 120 ………….. (iii)
x, y ≥ 0 ………….. (iv)
The feasible region determined by the system of constraints isgiven below
A (24, 0), B (8, 20) and C (0, 25) are the corner points
The values of Z at these corner points are given below
| Corner point | Z = 5x + 6y | |
| A (24, 0) | 120 | |
| B (8, 20) | 160 | Maximum |
| C (0, 25) | 150 | |
The maximum value of Z is 200 at (8, 20)
Hence, 8 souvenirs of type A and 20 souvenirs of type B shouldbe produced each day to get the maximum profit of Rs 160