Embibe Experts Solutions for Chapter: Linear Programming, Exercise 1: Gujarat Board-2018

Maximise $z=x+y$ subject to $x+y\le 1,-3x+y\ge 3 \text{and }x\ge 0,y\ge 0$, if possible?

The objective function of an LPP problem is

The corner points of the feasible region determined by the system of linear constraints are $(0,10),(5,5),(15,15),(5,25)$. Let $z=px+qy,\text{ where }p,q>0$. The condition on $p\text{ and }q$ so that the maximum of $z$ occurs at both points $(15,15) \text{and} (5,25)$ is 

Let $O\left(0, 0\right), A\left(35, 0\right), B\left(30, 10\right), C\left(15, 25\right)$ and $D\left(0, 30\right)$ be the vertices of the feasible region of $\mathrm{LP}$ problem. Find the maximum and minimum values of the objective function $z=300x+600y$.

The objective function of linear programming problem is _____.

The vertices of the feasible region determined by some linear constraints are $\left(0,2\right),\left(1,1\right),\left(3,3\right),\left(1,5\right)$. Let $Z=px+qy$, where $p,q>0$. The condition on $p$ and $q$ so that the maximum of $Z$ occurs at both the points $\left(3,3\right)$ and $\left(1,5\right)$ is _____.

If the vertices of the feasible region are $O\left(0,0\right), A\left(10,0\right), B\left(0,20\right), C\left(15,15\right)$, then the minimum value of the objective function $Z=10x-20y+30$ is

Solve the following linear programming problem graphically. Subject to the constraints : $x+y\le 50,3x+y\le 90,x\ge 0,y\ge 0$ obtain the maximum and minimum values of $Z=5x+10y$.