Question 1

If the number of available constraints is 3 and the number of parameters to be optimise is 4 , then

Accepted Answer

To optimised n number of parameters, we need atleast n constraints.

Question 2

Minimum value of Z=3 x+5 y subject to constraints x+y 2, x+3 y 3, x, y 0

Accepted Answer

Z is 7 minimum at ( 3 2 , 1 2 )

Question 3

The maximum value of z=5 x+2 y subject to constraints x+y 7, x+2 y 10, x, y 0

Accepted Answer

Change the inequalities into equations and draw the graph of lines, thus we get the required feasible region as shown below. The region bounded by the vertices A(0,5), B(4,3), C(7,0) The objective function is maximum at C (7,0) and Max z=5 7+2 0=35.

Question 4

The maximum value of z=6 x+8 y subject to constraints 2 x+y 30, x+2 y 24 and x 0, y 0 is

Accepted Answer

Here, 2 x+y 30, x+2 y 24, x, y 0 The shaded region represents the feasible region, hence z =6 x +8 y . Obviously it is maximum at (12,6) Hence z=12 6+8 6=120

Linear Programming — Previous Year Questions & Solutions