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  • Explain solution for RD Sharma Class 12 Chapter 29 Linear Programming Exercise Multiple Choice Question Question 18 maths textbook solution.

Explain solution for RD Sharma Class 12 Chapter 29 Linear Programming Exercise Multiple Choice Question Question 18 maths textbook solution.

Answers (1)

Answer : (d) \text{q = 3p}

Hint : Put (15,15) and (0,20) in \text {z = px + qy}

Given :  Linear constraints are (0,10),(5,5),(15,15),(0,20)

Let \text {z = px + qy} where \text {p,q}>0. \text {z}_{\text {max}} occurs at both points (15,15) and (0,20) ________

Solution :

\begin{aligned} &z_{\max (15,15)}=z_{\max (0,20)} \\ \end{aligned}

\begin{aligned} &p(15)+q(15)=p(0)+q(20) \\ \end{aligned}

\begin{aligned} &p(15)=q(20)-q(15) \\ \end{aligned}

\begin{aligned} &15 p=5 q \\ \end{aligned}

\begin{aligned} &3 p=q \end{aligned}

So, the correct option is (d)

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