Question

Consider the following linear program: Min 3A + 48 +28 26 AB 20 2. Select the correct graph that shows the feasible region and the optimal solution for the problem. 0 (1) 10 8 Optimal Solution: A-2, B-2 - Optional Solution And, BM A

Answer 1

Answer

a) option (i) is the correct answer

working:-

A + 2B = 6 .................................................(1)  

If,

A	B
0	3
6	0

As shown in the graph (i)

Now, if we put 0(zero) in place of A & B in the above equation then 0 + 0 $\ngeqslant$ 6

Therefore the are marked will be above the line.

Similarly,

A + B = 4........................................(2)

If,

a	b
0	4
4	0

As shown in the graph (i)

Now, if we put 0(zero) in place of A & B in the above equation then 0 + 0 $\ngeqslant$ 4

Therefore the are marked will be above the line.

So, the common area marked will be same as in option (i)

b) To find the value of the objective function:-

coordinates of the feasible region are = (0,4) (2,2) (6,0)

now putting these values in the objective function -

(0,4) = 3 (0) + 4(4) = 16

(2,2) = 3(2) + 4(2) = 14

(6,0) = 3(6) + 4(0) = 18

Since the (2,2) give the minimum value of 14 , therefore it is the value of objective function (or the optimal solution)