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51.

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

A(x)B(y)Max. time available
Cutter42208
Finisher24152
Profit75125

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
x052
y1040
(0, 104) (52, 0)
x + 2y = 76
x00
y3876
(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.
Discussion
52.

Feasible region is the set of points which satisfy _______.(A) the objective function (B) all of the given constraints (C) some of the given constraints (D) only one constraint

Answer»

Correct answer is (B) all of the given constraints
Discussion
53.

Of all the points of the feasible region, the optimal value ofz obtained at the point lies _______. (A) inside the feasible region (B) at the boundary of the feasible region (C) at vertex of feasible region (D) outside the feasible region

Answer»

Correct answer is (C) at vertex of feasible region
Discussion
54.

Solution of L.P.P. to minimize z = 2x + 3y such that x ≥ 0, y ≥ 0, 1 ≤ x + 2y ≤ 10 is _______.(A) x = 0, y = 1/2(B) x = 1/2, y = 0(C) x = 1, y = 2(D) x = 1/2, y = 1/2

Answer»

Correct answer is (A) x = 0, y = 1/2
Discussion