Question

A furniture shop keeper deals only Teak and Rosewood tables which costs Rs. $25,000$ and Rs. $40,000$ respectively. His shop can contain a maximum of $250$ tables. The profit that he gets on these items are respectively Rs. $4,500$ and Rs. $5000$.
He plans to invest a maximum of Rs. $70$ lakhs in his business.
(i) Formulate this problem.
(ii) Write the objective function if he wishes to make maximum profit.

Answer 1

Let $x$ and $y$ be the quantities of Teak and Rosewood tables respectively.

The shop can contain a maximum of $250$ tables.

$\Rightarrow x+y\le 250$

The shopkeeper can invest a maximum of Rs. $70,00,000$

$\Rightarrow 25000x+40000y\le 7000000$

$\Rightarrow 5x+8y\le 1400$

Hence, the mathematical formulation of this problem is:

$x+y\le 250$

$5x+8y\le 1400$

Since the shopkeeper wishes to maximize his profit, the objective function will be to maximize $Z:4500x+5000y$ subject to the following conditions:

$x+y\le 250$

$5x+8y\le 1400$