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  • Need solution for RD Sharma maths Class 12 Chapter 29 Linear Programming Exercise Multiple Choice Question Question 13 textbook solution.

Need solution for RD Sharma maths Class 12 Chapter 29 Linear Programming Exercise Multiple Choice Question Question 13 textbook solution.

Answers (1)

Answer : (b) x_{1}=2, x_{2}=6, z=36

Hint :

Convert the inequalities into equation

Given:  z_{\max }=3 x_{1}+5 x_{2}  Subject to the constraints are

\begin{aligned} &3 x_{1}+2 x_{2} \leq 18 \\ &x_{1} \leq 4 \\ &x_{2} \leq 6 \\ &x_{1} \geq 0, x_{2} \geq 0 \end{aligned}

Solution :

By the graphical method,

Now,

\begin{aligned} &3 x_{1}+2 x_{2} \leq 18 \\ &\frac{x_{1}}{6}+\frac{x_{2}}{9} \leq 1 \end{aligned}

Checking coordinates,

\begin{aligned} &\mathrm{At}(0,0) \rightarrow z=0 \\ \end{aligned}

\begin{aligned} &\mathrm{At}(4,0) \rightarrow z=12 \\ \end{aligned}

\begin{aligned} &\mathrm{At}(4,3) \rightarrow z=27 \\ \end{aligned}

\begin{aligned} &\mathrm{At}(2,6) \rightarrow z=36 \end{aligned}

\begin{aligned} &\mathrm{At}(0,6) \rightarrow z=30 \\ \end{aligned}

\begin{aligned} &z_{\max }=36_{\mathrm{at}}(2,6) \end{aligned}

So, the correct option is (b)

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