Question

A manufacturer can sell all he produces at ₹ 60 each. It costs ₹ 40 in materials and labour to produce each item and overhead expenses are ₹ 3000 per week. How many units should be produced and sold to make a profit of at least ₹ 1000 per week?

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

Hint:

Separate fixed and variable costs: Profit $=(\text{SP}-\text{VC})\times x-\text{Fixed}$. Then solve the linear inequality for $x$.

Answer 1

The Correct Option is D

Step 1: Write profit for $x$ units.
Revenue $=60x$, variable cost $=40x$, fixed overhead $=3000$.
\Rightarrow\ Profit $=60x-(40x+3000)=20x-3000$. Step 2: Impose the target.
$20x-3000\ge 1000 \Rightarrow 20x\ge 4000 \Rightarrow x\ge 200$.
At $x=200$, profit $=20\cdot 200-3000=₹ 1000$ (meets "at least").
\[ \boxed{200} \]