IGNOU MTE 12 2026 - Solve the following LPP graphically:Maximize:$subject to t

Question

Solve the following LPP graphically:

Maximize:

$$z = 10x_1 + 10x_2$ $
subject to the constraints:
$$4x_1 + 3x_2 \le 12$ $
$$6x_1 + 18x_2 \le 36$ $
$$x_1, x_2 \ge 0.$ $
b) Find all values of k for which the vectors:
$$\begin{bmatrix} 1 \\ 0 \\ 1 \end{bmatrix}, \begin{bmatrix} 0 \\ -1 \\ 1 \end{bmatrix} \text{ and } \begin{bmatrix} 2 \\ -k \\ 2k \end{bmatrix}$ $
are linearly independent.

09 Jan 2026

Answer :

Word Count : 171

The constraints are first plotted in the first quadrant. The line (4x_1+3x_2=12) cuts the axes at ((3,0)) and ((0,4)). The line (6x_1+18x_2=36), or equivalently (x_1+3x_2=6), cuts the axes at ((6,0)) and ((0,2)). With (x_1,x_2\ge0), the feasible region is the common area below both lines. The corner points of this region are ((0,0)), ((3,0)), ((0,2)), and the point of intersection of the two lines. Solving (4x_1+3x_2=12) and (x_1+3x_2=6)

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