Q.
Let $x$ and $y$ are the number of tables and chairs respectively, on which a furniture dealer wants to make profit for the constraints
$ \text { Maximise } Z=250 x+75 y$
$ 5 x+y \leq 100$
$ x+y \leq 60 $
$ x \geq 0 $
$ y \geq 0 $
Consider the following graph
Then, the maximum profit to the dealer results from buying
Linear Programming
Solution:
The graph of the given constraints is
The corner points (vertices) of the bounded (feasible) region are $O, A, B$ and $C$ and it is easy to find their coordinates as $(0,0),(20,0),(10,50)$ and $(0,60)$. respectively. Let us now compute the values of $Z$ at these points.
We have,
Vertex of the feasible region
Corresponding value of $Z$ (in ₹)
$O(0,0)$
0
$C(0,60)$
4500
$B(10,50)$
6250 $\longleftarrow$ Maximum
$A(20,0)$
5000
We observe that the maximum profit to the dealer results from the investment strategy $(10,50)$, i.e., buying 10 tables and 50 chairs.
This method of solving linear programming problem is referred as corner point method.
| Vertex of the feasible region | Corresponding value of $Z$ (in ₹) |
|---|---|
| $O(0,0)$ | 0 |
| $C(0,60)$ | 4500 |
| $B(10,50)$ | 6250 $\longleftarrow$ Maximum |
| $A(20,0)$ | 5000 |