Questions & Answers

Question

Answers

Answer
Verified

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.

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.

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.