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  • Feasible region (shaded) for a LPP is shown in Fig. 12.8. Maximise Z = 5x + 7y.

Q: Feasible region (shaded) for a LPP is shown in Fig. 12.8. Maximise Z = 5x + 7y.\\

Answers (1)

Following is the equation:

Z=5x+7y

The region that is shaded is OABD in the diagram that is being given. The maximum value of the corner point will occur at the feasible point.

When we substitute these values in Z, we get the corner points, we get:

\begin{array}{|l|l|} \hline \text { Corner Point } & \text { Value of } \mathrm{Z}=5 \mathrm{x}+7 \mathrm{y} \\ \hline \mathrm{O}(0,0) & \mathrm{Z}=5(0)+7(0)=0+0=0 \\ \mathrm{~A}(7,0) & \mathrm{Z}=5(7)+7(0)=35+0=35 \\ \mathrm{~B}(3,4) & \mathrm{Z}=5(3)+7(4)=15+28=43 \rightarrow \max \\ \mathrm{D}(0,2) & \mathrm{Z}=5(0)+7(2)=0+14=14 \\ \hline \end{array}

Therefore, the final answer is the maximum value of Z is 43 at the point (3,4)

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