Linear Programming

Optimization of the objective function is a process of

Corner points of feasible region of inequalities gives

The feasible solution of L.P.P. belongs to

The feasible region of the linear programming problems is determined by the system of inequalities: $x+y\leq 6,x\geq 0,y\geq 0$. The maximum value of $x+y$ in the feasible region is

The point at which the maximum value of $(3 x+2 y)$ subject to the constraints $x+y \leq 2, x \geq 0, y \geq 0$ is obtained, is

Maximize $z=2x+3y$

Subject to the constraints $x+y\geq 2,x+2y\geq 3,x,y\geq 0$.

The maximum value of $P=x+3y$ such that $2x+y\leq 20,x+2y\leq 20,x\geq 0,y\geq 0$ is

A manufacturer produces nuts and bolts for industrial machinery. It takes 1 hour of work on machine A and 3 hours on machine B to produce a package of nuts, while it takes 3 hours on machine A and 1 hour on machine B to produce a package of bolts. He earns a profit of ₹ 2.50 per package on nuts and ₹ 1 per package on bolts. Form a linear programming problem to maximize his profit, if he operates each machine for atmost 12 hours.

A manufacturing company produces two items, A and B. Each toy should be processed by two machines, I and II. Machine I can be operated for maximum 10 hours 40 minutes. It takes 20 minutes for an item of A and 15 minutes for B. Machine II can be operated for a total time at 8 hours 20 minutes. It takes 5 minutes for an item A and 8 minutes for B . The profit per item of $A$ is $R s 25$ and per item of $B$ is ₹ 18 . The formulation of an L.P.P. to maximize the profit (where $x$ is number of items A and $y$ is the number of item $B$ ) is

The shaded area in the given figure is a solution set for some system of inequalities. The maximum value of the function $\mathrm{z}=4 x+3 y$ subject to linear constraints given by the system is

Maximize $z=3x_{1}+4x_{2}$, if possible, Subject to the constraints

$x_{1}-x_{2}\leq-1,-x_{1}+x_{2}\leq 0;x_{1},x_{2}\geq 0$.

Maximize $z=7x_{1}-3x_{2}$

Subject to, $x_{1}+2x_{2}\leq 2,2x_{1}+4x_{2}\geq 8,x_{1}\geq 0,x_{2}\geq 0$.

Maximize $z=2x+5y$

Subject to the constraints $x+y\leq 4,3x+3y\geq 18,x,y\geq 0$.

Maximize $z=3x+2y$, subject to $x-y\leq 1,x+y\geq 3,x,y\geq 0$

Maximize $z=3x+4y$, if possible, subject to the constraints $x-y\leq-1,-x+y\leq 0,x,y\geq 0$