Question

A furniture dealer deals in only two items – tables and chairs. He has Rs. 50,000 invested and has storage space of at most 60pieces. A table costs Rs. 2500 and chair Rs. 500. He estimates that from the sales of one table, he can make a profit of Rs.250 and that from the sale of one chair a profit of Rs. 75. How many tables and chairs he should buy from the available money to maximize his total profit assuming that he can sell all the items which he buys.

Answer 1

Hint:
In this type of question we should first identify the constraint, variable and profit function. Always begin with the variable. In the above question table and chair numbers are treated as variable and the initial invested money is Rs 50,000. The dealer has a storage of 60 pieces. Each of the table and chair have specific cost and both of them make a specific profit.

Complete step by step solution:
The given data may be put in the following tabular form:

Suppose x units of table and y unit of chair he buys from the available money
Here is the profit function
Profit function: \[\]$Z=250X+75Y$
Total cost \[2500x+500y\le 50000\]
But the storage capacity is max 60 items

Here are three critical points A(10,50) ,C(20,0) ,D(0,60)
For point A $Z=250X10+75X50=6520$
For point C \[Z=250X20+75X0=5000\]
For point D $Z=250X0+75X60=4500$
He should buy 10 tables and 50 chairs for obtaining maximum profit.

Note:
This type of question is very important from an examination point of view and is often asked in board examinations. Students are requested to draw the graph of the above question in a graph paper. In these types of questions recognizing critical points and calculating maximum profit value is the crucial step.