A company has a fixed cost of INR 3,00,000 and a variable cost of INR 150 per unit for manufacturing of a product. The company sells 5,000 units of that product making a profit equivalent to 20% of the total sales revenue.
The break-even quantity for that product is _____ units (rounded off to the nearest integer).

Question

A through hole of 10 mm diameter is to be drilled in a mild steel plate of 30 mm thickness. The selected spindle speed and feed for drilling hole are 600 revolutions per minute (RPM) and 0.3 mm/rev, respectively. Take initial approach and breakthrough distances as 3 mm each. The total time (in minute) for drilling one hole is ______. (Rounded off to two decimal places)

Answer 1

Step 1: Understanding the Concept:
We need the Break-Even Point (BEP) in units. Since the selling price is not stated directly, we first find it from the profit condition given in the problem.

Step 2: Key Formula or Approach:
Total Cost, $TC = FC + v \times Q$.
Total Revenue, $TR = P \times Q$.
Profit $= TR - TC$, and break-even quantity $= \dfrac{FC}{P - v}$.

Step 3: Detailed Explanation:
First compute the total cost at the given sales volume of 5000 units:
\[ TC = 300000 + (150 \times 5000) = 300000 + 750000 = 1050000 \]
Since profit is 20% of revenue, the cost portion is the remaining 80% of revenue:
\[ 0.8 \times TR = TC = 1050000 \]
\[ TR = \frac{1050000}{0.8} = 1312500 \]
The selling price per unit is then:
\[ P = \frac{TR}{Q} = \frac{1312500}{5000} = 262.5 \]
Now the break-even quantity:
\[ Q_{BEP} = \frac{300000}{262.5 - 150} = \frac{300000}{112.5} = 2666.67 \]

Final Answer:
Rounding off to the nearest integer, the break-even quantity is 2667 units.
\[ \boxed{Q_{BEP} = 2667 \text{ units}} \]

Show Hint

Correct Answer: 2667

Solution and Explanation

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