List of top Mathematics Questions on Linear Programmig Problem

The corner points of the feasible region determined by $x + y \leq 8$, $2x + y \geq 8$, $x \geq 0$, $y \geq 0$ are $A(0, 8)$, $B(4, 0)$, and $C(8, 0)$. If the objective function $Z = ax + by$ has its maximum value on the line segment $AB$, then the relation between $a$ and $b$ is:
Which one of the following represents the correct feasible region determined by the following constraints of an LPP?
\[ x + y \geq 10, \quad 2x + 2y \leq 25, \quad x \geq 0, \quad y \geq 0 \]
\(\text{The feasible region represented by the constraints } 4x + y \geq 80, \; x + 5y \geq 115, \; 3x + 2y \leq 150, \; x, y \geq 0 \; \text{of an LPP is:}\)
Problem figure
Solve the following linear programming problem graphically: Maximise \( Z = 2x + 3y \), subject to the constraints: \( x + y \leq 6, \, x \geq 2, \, y \geq 3, \, x \geq 0, \, y \geq 0. \)

Assertion (A): The corner points of the bounded feasible region of a L.P.P. are shown below. The maximum value of \( Z = x + 2y \) occurs at infinite points. 
Reason (R): The optimal solution of a LPP having bounded feasible region must occur at corner points. 
 

Graph Content

The maximum value of \( Z = 4x + y \) for a L.P.P. whose feasible region is given below is: 
 

Graph for region
(b) Evaluate: \[ \int_{1}^{3} \left(|x - 1| + |x - 2| + |x - 3|\right) \, dx. \]
A linear programming problem deals with the optimization of a/an: