Let x and y be the number of tables and chairs.
cost of x table = Rs. 250 and cost of y chair = Rs. 50
Since the dealer is maximum invest Rs. 5000 and the maximum number of items.
Also, the dealer want to sell a table and chair at the profit Rs. 50 and Rs. 15 respectively.
So, from the above explanation, we get following mathematical form as follows
250x + 50y ≤ 5000
5x + y ≤ 100
x + y ≤ 60, x ≥ 0,y ≥ 0
and objective function Z = 50x + 15y
Now, we have to maximize Z = 50x + 15y
Subject to constraints
Now, to solve first of all draw a graph of equation ( l) to (3) corresponds to- in equations. It is clear from the graph that OABC be a feasible region, which is bounded. The co-ordinates of corner points of feasible region are O(0, 0), A(20, 0), B(10,50). The co-ordinate of the point B we get by solving equations (1) and (2). Lastly, applying corner point method to find maximum values of objective function Z as follows :
It is clear from above table the maximum values of Z is 125O at the point (10, 50). Thus the maximum profit to the dealer is Rs. 1250 for buying 10 tables and 50 chairs.