Vinod Singh and Shweta Pawar Solutions for Chapter: Linear Programming, Exercise 4: Evaluation Test

All points lying inside the triangle formed by the points $\left(1,3\right),\left(5,0\right)$ and $\left(-1,2\right)$ satisfy

The linear programming problem: Maximize $z=x_1+x_2$ subject to constraints $x_1+2x_2\le 2000, x_1+x_2\le 1500, 0\le x_2\le 600, x_1\ge 0$  has

The solution of set of constraints $x+2y\ge 11, 3x+4y\le 30, 2x+5y\le 30, x\ge 0, y\ge 0$ includes the point

A manufacturer is preparing a production plan on medicines $A$ and $B$. There are sufficient ingredients available to make $20,000$ bottles of $A$ and $40,000$ bottles of $B$ but there are only $45,000$ bottles into which either of the medicines can be put. Further it takes $3$ hours to prepare enough material to fill $1000$ bottles of $A$. It takes one hour to prepare enough material to fill $1000$ bottles of $B$ and there are $66$ hours available for this operation. The number of constraints the manufacturer has is

A company manufactures two types of telephone sets $A$ and $B$. The A type telephone set requires $2$ hour and $B$ type telephone requires $4$ hour to make. The company has $800$ work hours per day. $300$ telephones can pack in a day. The selling prices of $A$ and $B$ type telephones are $₹300$ and $400$ respectively. For maximum profits company produces $x$ telephones of $A$ type and $y$ telephones of $B$ types. Then except $x\ge 0$ and $y\ge 0$, linear constraints and the probable region of the $\mathrm{LPP}$ is of the type

The feasible region of the constraints $4x+2y\le 8, 2x+5y\le 10$ and $x, y\ge 0$ is

The $\mathrm{LPP}$ problem Max. $z=x_1+x_2$ such that $-2x_1+x_2\le 1, x_1\le 2, x_1+x_2\le 3$ and $x_1, x_2\ge 0$ has

For the $\mathrm{L}.\mathrm{P}.\mathrm{P}.$ problem, the maximum value of the function, $z=3x+2y$ subject to $x+y\ge 1, y-5x\le 0, x-y\ge -1, x+y\le 6, x\le 3$ and $x,y\ge 0$, is/are