Question

a company makes rattan and plastic chairs. it the rattan and plastic chairs are sold at p220 and p150, respectively, how many of each chair are to be sold for the company to make a revenue of more than p3,700​

Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

A company makes rattan and plastic chairs. it the rattan and plastic chairs are sold at p220 and p150, respectively.

Let assume that

Number of rattan sold be x units

Number of plastic chairs sold be y units.

As Given that,

Selling Price of one rattan = p220

So,

Selling Price of x rattan = p220x

Also,

Selling Price of 1 plastic chair = p150

So,

Selling Price of y plastic chairs = p150y

So, it means

Total revenue received = 220x + 150y

According to statement,

Total revenue received > p3700

$\rm \: 220x + 150y > 3700$

$\rm\implies \:22x + 15y > 370$

Now, to solve this inequality, we take the help of graphical method and the half plane contains the solution set of this inequality.

Let first sketch the line

$\rm \: 22x + 15y = 370$

Substituting 'x = 1' in the given equation, we get

$\rm \: 22 \times 1+ 15y = 370$

$\rm \: 22 + 15y = 370$

$\rm \: 15y = 370 - 22$

$\rm \: 15y = 348$

$\rm\implies \:y = 23.2$

Substituting 'x = - 5' in the given equation, we get

$\rm \: 22 \times ( - 5)+ 15y = 370$

$\rm \: - 110+ 15y = 370$

$\rm \: 15y = 370 + 110$

$\rm \: 15y = 480$

$\rm\implies \:y = 32$

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 1 & \sf 23.2 \\ \\ \sf - 5 & \sf 32 \\ \\ \sf 4 & \sf 18.8 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points.

➢ See the attachment graph.

Now, from graph we concluded that

If we sold 10 rattan and 12 plastic chairs, the revenue is more than 3700.

So,

Number of rattan sold = 10

Number of plastic chairs sold = 12

[ Remark :- There are infinite positive integers for which revenue is more than 3700, its one of the solution ]