A person makes two types of gift items A and B requires the services of a cutter and a finisher. Gift item A requires 4 hours of cutter’s time
A person makes two types of gift items A and B requires the services of a cutter and a finisher. Gift item A requires 4 hours of cutter’s time and 2 hours of finisher’s time. B requires 2 hours of cutter’s time and 4 hours of finisher’s time. The cutter and finisher have 208 hours and 152 hours available times respectively every month. The profit of one gift item of type A is Rs 75/- and on gift item B is Rs 125/-. Assuming that the person can sell all the gift items produced, determine how many gift items of each type should he make every month to obtain the best returns?
1 Answers
Let x : number of gift item A
y : number of gift item B
As numbers of the items are never negative x ≥ 0; y ≥ 0
| A(x) | B(y) | Max. time available | |
| Cutter | 4 | 2 | 208 |
| Finisher | 2 | 4 | 152 |
| Profit | 75 | 125 |
Total time required for the cutter = 4x + 2y
Maximum available time 208 hours
∴ 4x+ 2y ≤ 208
Total time required for the finisher 2x +4y
Maximum available time 152 hours
2x + 4y ≤ 152
Total Profit is 75x + 125y
∴ L.P.P. of the above problem is
Minimize z = 75x + 125y
Subject to 4x+ 2y ≤ 208
2x + 4y ≤ 152
x ≥ 0; y ≥ 0
Graphical solution
| 2x + y = 104 | ||
| x | 0 | 52 |
| y | 104 | 0 |
| (0, 104) (52, 0) | ||
| x + 2y = 76 | ||
| x | 0 | 0 |
| y | 38 | 76 |
| (0, 38) (76, 0) | ||
Corner points
Now, Z at
x = (75x + 125y)
O(0, 0) = 75 × 0 + 125 × 0 = 0
A(52,0) = 75 × 52 + 125 × 0 = 3900
B(44, 16) = 75 × 44 + 125 × 16 = 5300
C(0, 38) = 75 × 0 + 125 × 38 = 4750
A person should make 44 items of type A and 16 Uems of type Band his returns are Rs 5,300.