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

Find the maximum value of $Z = 3 x + 2 y$ by graphical method of solving linear programming problem under the following constraints.

$x + y ⩽ 7, 2 x + 3 y ⩽ 16, x ⩾ 0, y ⩾ 0$

Accepted Answer

Given,

$Z = 3 x + 2 y$

Now, take $x + y = 7$ ...(i)

$\begin{matrix} x & 0 & 7 \\ y & 7 & 0 \end{matrix}$

For $2 x + 3 y = 16$

$\begin{matrix} x & 0 & 8 \\ y & \frac{16}{3} & 0 \end{matrix}$

Let us draw the graph for the above points

Now, we need check maximum value from the corner points.

From the graph at $(0, \frac{16}{3})$ , value of $Z = 3 (0) + 2 (\frac{16}{3}) = \frac{32}{3}$

At the point $(5, 2)$ , value of $Z = 3 (5) + 2 (2) = 19$

At the point $(7, 0)$ , value of $Z = 3 (7) + 2 (0) = 21$

Thus, the maximum value of $Z$ is $21$ .

Find the maximum value of $Z = 3 x + 2 y$ by graphical method of solving linear programming problem under the following constraints.

$x + y ⩽ 7, 2 x + 3 y ⩽ 16, x ⩾ 0, y ⩾ 0$

Important Questions on Linear Programming

Learn and Prepare for any exam you want !

Find the maximum value of Z=3x+2y by graphical method of solving linear programming problem under the following constraints. x+y⩽7,2x+3y⩽16,x⩾0,y⩾0

Important Questions on Linear Programming

Learn and Prepare for any exam you want !

Find the maximum value of $Z = 3 x + 2 y$ by graphical method of solving linear programming problem under the following constraints.

$x + y ⩽ 7, 2 x + 3 y ⩽ 16, x ⩾ 0, y ⩾ 0$