Question

Let $x$ and $y$ are the number of tables and chairs respectively, on which a furniture dealer wants to make profit for the constraints
$\text{ Maximise }Z=250x+75y$
$5x+y\le 100$
$x+y\le 60$
$x\ge 0$
$y\ge 0$
Consider the following graph

Then, the maximum profit to the dealer results from buying

• A. 10 tables and 50 chairs
• B. 50 tables and 10 chairs
• C. 0 table and 60 chairs
• D. 20 tables and 40 chairs

Answer 1

Answer: (A)

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 $⟵$ 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.