Break-even analysis between two manufacturing alternatives Two alternatives can produce the same product. Method 1: fixed cost = Rs. 2,000, variable cost = Rs. 20 per piece. Method 2: fixed cost = Rs. 1,500, variable cost = Rs. 30 per piece. At what output quantity (pieces) do the total costs break even between the two methods?

Introduction / Context:
Break-even analysis compares alternatives with different fixed and variable costs to find the output level at which their total costs are equal. This is fundamental in process selection, make-or-buy decisions, and capacity planning.

Given Data / Assumptions:

• Method 1: F1 = 2000 Rs, V1 = 20 Rs/piece.
• Method 2: F2 = 1500 Rs, V2 = 30 Rs/piece.
• Both methods produce identical quality and sell at the same price (revenue is irrelevant to cost-only break-even between alternatives).

Concept / Approach:
Total cost TC = Fixed cost + Variable cost * Quantity. Break-even quantity Q* is obtained by equating total costs of both methods and solving for Q.

Step-by-Step Solution:
Write total costs: TC1 = 2000 + 20Q; TC2 = 1500 + 30Q.Equate: 2000 + 20Q = 1500 + 30Q.Rearrange: 2000 - 1500 = 30Q - 20Q → 500 = 10Q.Solve: Q = 500 / 10 = 50 pieces.

Verification / Alternative check:
Compute totals at Q = 50: TC1 = 2000 + 2050 = 2000 + 1000 = 3000 Rs; TC2 = 1500 + 30*50 = 1500 + 1500 = 3000 Rs. Costs match, confirming the break-even.

Why Other Options Are Wrong:
25, 75, 100, 150 pieces do not satisfy the equality TC1 = TC2; substituting any of these values yields different totals.

Common Pitfalls:
Mixing contribution or price into a cost-only comparison; forgetting units; transposing fixed and variable costs; arithmetic mistakes when rearranging terms.

Final Answer:
50