Saved Bookmarks
| 1. |
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? |
||||||||||||||||||||||||||||||||||||||||
|
Answer» 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
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
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. |
|||||||||||||||||||||||||||||||||||||||||