Question

The feasible region of an LPP is shown in the figure. If Z = 11x + 7y then the maximum value of Z occurs at

• A. (0, 5)
• B. (3, 3)
• C. (5, 0)
• D. (3, 2)

Answer 1

The Correct Option is D

The feasible region of an LPP is shown in the figure. If \(Z = 11x + 7y\), then we need to find the maximum value of Z and where it occurs.

\(x + y = 5\) and \(x + 3y = 9\)

Subtract the first equation from the second:

\((x + 3y) - (x + y) = 9 - 5\)

\(2y = 4\)

\(y = 2\)

Substitute y = 2 into the first equation:

\(x + 2 = 5\)

\(x = 3\)

So, the point of intersection is (3, 2).

Now we evaluate Z at the key vertices (3, 2)

If( x +y=5 so 3 + 2 =5, so if points IS (55 It should be : (55),3) and that point ,must verify that it is an feasible points.

At (3, 2): \(Z = 11(3) + 7(2) = 33 + 14 = 47\)

The maximum value of Z is 47, which occurs at (3, 2)

Therefore, ,the correct option is indeed :(D) (3, 2).