Solution Steps

To determine the number of units needed to achieve a specific profit target, we calculate the contribution margin per unit and then use the profit equation.

1. Calculate Contribution Margin per Unit

The contribution margin per unit is the difference between the selling price per unit and the variable cost per unit. This indicates the amount each unit contributes towards covering fixed costs and generating profit.

Formula: $CM_{unit} = SP_{unit} - VC_{unit}$

Given:

• Selling Price per unit ($SP_{unit}$) = ₹56.00
• Variable Cost per unit ($VC_{unit}$) = ₹32.00

Calculation: $CM_{unit} = ₹56.00 - ₹32.00 = ₹24.00$

2. Calculate Required Units for Target Profit

The total profit is the total contribution margin generated from sales minus the total fixed costs. The formula can be rearranged to solve for the number of units (Q) required.

Profit Equation: Total Profit ($P$) = ($CM_{unit} \times Q$) - Total Fixed Cost ($FC$)

Rearranged Formula for Units (Q): $Q = \frac{P + FC}{CM_{unit}}$

Given:

• Target Profit ($P$) = ₹84,000
• Total Fixed Cost ($FC$) = ₹60,000
• Contribution Margin per Unit ($CM_{unit}$) = ₹24.00

Calculation:

$Q = \frac{₹84,000 + ₹60,000}{₹24.00}$

$Q = \frac{₹144,000}{₹24.00}$

$Q = 6000$ units

Result

Selling 6000 units will achieve the target profit of ₹84,000.