# Consider the following problem. Maximize Z = 3x_1 + 2x_2 S.T. 2x_1 + x_2 less

Consider the following problem. Maximize Z = 3x_1 + 2x_2 S.T. 2x_1 + x_2 less thanorequalto 6 x_1 lessthanorequalto 2 x_2 lessthanorequalto 4 x_1, x_2 greaterthanorequalto 0 Plot the problem and circle all CPF solutions

After making equality,

2X1 + X2 = 6

If X1 = 0

X2 = 6

If X2 = 0

X1 = 3

Further

X1 ≤ 2

X2 ≤ 4

Possible solutions for (X2, X1) are: (0, 2) , (2, 2) , (4, 1) and (4, 0)

Maximize Z = 3X1 + 2X2

At (0, 2)

Z = 3*2 + 2*0 = 6

At (2, 2)

Z = 3*2 + 2*2 = 10

At (4, 1)

Z = 3*1 + 2*4 = 11

At (4, 0)

Z = 3*0 + 2*4 = 6

Since, the Z is maximized at (4, 1) and X1 and X2 fulfils all the constraint conditions. Then it is the best solution.

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