Name: Linear Programming: Manufacturing Problem
Uploaded: 2019-07-19
Duration: 7 min 3 s
Description: In this video we are going to learn linear programming manufacturing problem comprehensively with the help of real life examples. Check it out!

Question

Solve the Linear Programming Problem graphically ;

Maximize and Minimize $z = 6 x + 3 y$ subject to $4 x + y \geq 80$ , $x + 5 y \geq 115$ , $3 x + 2 y \leq 150$ , $x \geq 0, y \geq 0$

Accepted Answer

The given constraints are

$4 x + y \geq 80$

$4 x + y \geq 80$

$3 x + 2 y \geq 150$

$x, y \geq 0$

Converting the given in-equations into equations, we get

$4 x + y = 80, x + 5 y = 115, 3 x + 2 y = 150, x = 0$ and $y = 0$

These lines are drawn on the graph and the shaded region $A B C$ represents the feasible region of the given $L P P$

It can be observed that the feasible region is bounded. The coordinates of the corner points of the feasible region are $A (2, 72), B (15, 20)$ and $C (40, 15)$

Corner point Value of the objective function $Z = 6 x + 3 y$

$A (2, 72)$ $Z = 6 \times 2 + 3 \times 72 = 228$

$B (15, 20)$ $Z = 6 \times 15 + 3 \times 20 = 150$

$C (40, 15)$ $Z = 6 \times 40 + 3 \times 15 = 285$

From the table, $Z$ is minimum at $x = 15$ and $y = 20$ and the minimum value of $Z$ is $150$

$∴$ The minimum value of $Z$ is $150$

Solve the Linear Programming Problem graphically ;

Maximize and Minimize $z = 6 x + 3 y$ subject to $4 x + y \geq 80$ , $x + 5 y \geq 115$ , $3 x + 2 y \leq 150$ , $x \geq 0, y \geq 0$

Important Questions on Linear Programming

Learn and Prepare for any exam you want !

Solve the Linear Programming Problem graphically ; Maximize and Minimize z=6x+3y subject to 4x+y≥80, x+5y≥115, 3x+2y≤150, x≥0,y≥0

Important Questions on Linear Programming

Learn and Prepare for any exam you want !

Solve the Linear Programming Problem graphically ;

Maximize and Minimize $z = 6 x + 3 y$ subject to $4 x + y \geq 80$ , $x + 5 y \geq 115$ , $3 x + 2 y \leq 150$ , $x \geq 0, y \geq 0$