Chapter 10.FOM, Problem 1P

PROBLEMS

1-4 ■ Find the maximum and minimum values of the given objective function on the indicated feasible region.

$M=200-x-y$

To determine

To find:

The maximum and minimum values of the given objective function on the indicated feasible region.

Answer to Problem 1P

Solution:

The maximum and minimum values of the objective function $M=200-x-y$ are $198$ and $195$ respectively

Explanation of Solution

Given:

The figure is,

Figure $\left(1\right)$

The objective function is,

$M=200-x-y$ …$\left(1\right)$

Approach:

Substitute the value of vertices in given equation $\left(1\right)$.

Calculation:

From the given figure,

The vertices are $\left(4,0\right)$, $\left(0,5\right)$ and $\left(0,2\right)$.

Make a table of $M$,

Vertices	$M=200-x-y$
$\left(4,0\right)$	$200-4-0=196$
$\left(0,5\right)$	$200-0-5=195$
$\left(0,2\right)$	$200-0-2=198$

Table $\left(1\right)$

From above table $\left(1\right)$, the maximum and minimum values of the objective function $M=200-x-y$ are $198$ and $195$ respectively.

Conclusion:

Hence, the maximum and minimum values of the objective function $M=200-x-y$ are $198$ and $195$ respectively $\left(0,6\right)$.