Question

The manufacturer of a certain item can sell all he can produce at the selling price of $\mathrm{Rs}.60$ each. It costs him $\mathrm{Rs}.40$ in materials and labour to produce each item and he has overhead expenses of $\mathrm{Rs}.3000$ per week in order to operate the plant. The number of units he should produce and sell in order to make a profit of at least $\mathrm{Rs}.1000$ per week is:

• A. $200$
• B. $250$
• C. $300$
• D. $400$

Answer 1

The correct option is A

$200$

Number of item produce per weak to make profit of $\mathrm{Rs}.1000$

The explanation for the correct option:

Option A. $200$

Let us consider the manufacturer produce $x$ items

The overhead expenses of a week is $\mathrm{Rs}.3000$

Then, the total cost of $x$ itemsis :

$\mathrm{Cost}P\mathrm{rice}(\mathrm{C}.\mathrm{P}.)=\mathrm{Rs}.(40x+3000)$

Since the item can sell all he can produce at the selling price of $\mathrm{Rs}.60$ each

Hence,$\mathrm{Selling}\mathrm{Price}(\mathrm{S}.\mathrm{P}.)=\mathrm{Rs}.60\mathrm{x}$

Calculate No. of item produced to make profit of $\mathrm{Rs}.1000$ as follow:

$$\begin{gathered} \because \mathrm{S}.\mathrm{P}.-\mathrm{C}.\mathrm{P}.=\mathrm{Profit} \\ \therefore 60x-(40x+3000)=1000 \\ \Rightarrow 60x-40x-3000=1000 \\ \Rightarrow 20x=1000+3000 \\ \Rightarrow 20x=4000 \\ \Rightarrow x=\frac{4000}{20} \\ \Rightarrow x=200 \end{gathered}$$

Thus, the manufacturer must produce $200$ items.

Thus, the correct option is option A.