Vinod Singh and Shweta Pawar Solutions for Chapter: Linear Programming, Exercise 3: Competitive Thinking

The co-ordinates of the point for minimum value of $z=7x-8y$ subject to the conditions $x+y-20\le 0, y\ge 5, x\ge 0, y\ge 0$ is

Solution of the $\mathrm{LPP}$ minimise $z=5x+10y$ subject to $x+2y\le 120, x+y\ge 60, x-2y\ge 0, x, y\ge 0$ is

The objective function $z=4x_1+5x_2$, subject to $2x_1+x_2\ge 7, 2x_1+3x_2\le 15, x_2\le 3, x_1, x_2\ge 0$ has minimum value at the point 

The objective function $z=x_1+x_2$, subject to $x_1+x_2\le 10, -2x_1+3x_2\le 15, x_1\le 6, x_1, x_2\ge 0$ has maximum value _____ of the feasible region.

Minimize $z=30x+20y$ subject to $x+y\le 8, x+2y\ge 4, 6x+4y\ge 12, x\ge 0, y\ge 0$

The maximum value of $z=4x+3y$ subject to the constraints $3x+2y\ge 160, 5x+2y\ge 200, x+2y\ge 80$; $x, y\ge 0$ is

For the $\mathrm{LPP}$, maximize $z=x+4y$ subject to the constraints $x+2y\le 2, x+2y\ge 8, x, y\ge 0$

The maximum value of $z=4x+2y$ subject to the constraints $2x+3y\le 18, x+y\ge 10, x, y\ge 0$, is