Chat with tutor

Ask Questions, Get Answers

Questions  >>  CBSE XII  >>  Math  >>  Linear Programming

The feasible solution for a LPP is shown in fig.12.12.Let $Z=3x-4y$ be the objective function.(Maximum value of $Z$+Minimum value of $Z$) is equal to

\[(A)13 \quad (B)\; 1\quad (C)\;-13 \quad (d)\;-17\]

1 Answer

  • Let $R$ be the feasible region for a linear programming problem and let $z=ax+by$ be the objective function.When $z$ has an optimum value (maximum or minimum),where variables $x$ and $y$ are subject to constraints described by linear inequalities,this optimum value must occur at a corner point of the feasible region.
  • If R is bounded then the objective function Z has both a maximum and minimum value on R and each of these occur at corner points of R
Step 1:
The objective function is $Z=3x-4y$
The corner points are $(0,0),(5,0),(6,5),(4,10),(0,8)$
For the points $(x,y)$ the objective function subject to $Z=3x-4y$
Step 2:
At $(0,0)$ the objective function $Z=3x-4y\Rightarrow Z=0$
At $(5,0)$ the objective function $Z=3x-4y\Rightarrow 3\times 5-4\times 0=15$
At $(6,5)$ the objective function $Z=3x-4y\Rightarrow 3\times 6-4\times 5=-2$
At $(6,8)$ the objective function $Z=3x-4y\Rightarrow 3\times 6-4\times 8=-14$
At $(4,10)$ the objective function $Z=3x-4y\Rightarrow 3\times 4-4\times 10=-28$
At $(0,8)$ the objective function $Z=3x-4y\Rightarrow 3\times 0-4\times 8=-32$
Step 3:
The maximum value of $Z$ is 15
The minimum value of $Z$ is -32
Hence the maximum value of $Z$+minimum value of $Z$ is $15-32=-17$
Correct option is $D$
Help Clay6 to be free
Clay6 needs your help to survive. We have roughly 7 lakh students visiting us monthly. We want to keep our services free and improve with prompt help and advanced solutions by adding more teachers and infrastructure.

A small donation from you will help us reach that goal faster. Talk to your parents, teachers and school and spread the word about clay6. You can pay online or send a cheque.

Thanks for your support.
Please choose your payment mode to continue
Home Ask Homework Questions
Your payment for is successful.
Clay6 tutors use Telegram* chat app to help students with their questions and doubts.
Do you have the Telegram chat app installed?
Already installed Install now
*Telegram is a chat app like WhatsApp / Facebook Messenger / Skype.