Question

For the given L.P.P

M ax(Z) = 2x + 2y
Subject to
x + y ≤ 1
x, y ≥ 0

The above problem has
(a) infeasible solution
(b) unbounded solution
(c) unique solution
(d) multiple optimal solution

Answer 1

(a)

Z=3x+2y (i)

subject to the constraints

x+2y≤10

3x+y≤15

Convert these inequalities into equations

x+2y=10 (ii)

3x+y=15 (iii)

From (ii), we get

x=0⟹y=5 and y=0 when x=10

So, the points (0,5) and (10,0) lie on the line given in (ii)

From (iii), we get the points

(0,15) and (5,0)

Let's plot these point and we get the graph in which, shaded part shows the feasible region.

(b)

Lines (ii) and (iii) intersect at (4,3) and other corner points of the region are (0,5),(5,0) and (0,0).

(c)

To find the maximum value of z, we need to find the value of z at the corner points

Corner points z=3x+2y

(0,0) 0

(5,0) 15

(0,5) 10

(4,3) 18

Thus, z is maximum at (4,3) and its maximum value is 18.

solution