Question

Under what condition linear programming has more than one optimal solution

Answer 1

Answer:

The multiple optimal solutions will arise in a linear program with more than one set of basic solutions that can minimize or maximize the required objective function. Sometimes, the multiple optimal solutions are called the alternative basic solution.

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Answer 2

Explanation:

Answer:

I hope this answer will help you .

Step-by-step explanation:

(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