Question

A Furniture dealer deals in only two items, table and chair. He has $Rs.5000$ to invest and a space to store at most $60$ pieces. A table costs him $Rs.250$ and a chair $Rs.50$. He can sell a table at a profit of $Rs.50$ and a chair at a profit of $Rs.15$. Assume that, he can sell all the items that he produced. The number of constraints in the problem is

• A. $2$
• B. $3$
• C. $4$
• D. $5$

Answer 1

The correct option is C

$4$

Explanation for the correct answer:

Step 1: Finding the investment equation

Let $x$ be the number of tables and $y$ be the number of chairs.

The cost of a table = $Rs.250$

The cost of the chair = $Rs.50$

The total investment of the dealer = $Rs.5000$

From the above statements the equation can be,

$$\begin{gathered} 250x+50y\le 5000 \\ 5x+y\le 100 \end{gathered}$$

Step 2: Finding the profit equation

The profit per table = $Rs.50$

The profit per chair = $Rs.15$

Let $Z$ be the total profit.

Then the objective function is,

$Z=50x+15y$.

Step 3: Finding the number of constraints

The dealer sells all the items that he produced.

Thus to maximize the profit $Z=50x+15y$,

The subjective constraints are

$$\begin{gathered} \Rightarrow 5x+y\le 100, \\ \Rightarrow x+y\le 60, \\ \Rightarrow x\ge 0and \\ \Rightarrow y\ge 0 \end{gathered}$$

Hence, option (C) is the correct answer.