Question

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 1

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.