Questions: Given the current sales volume and cost structure, determine the unit selling price required to achieve an annual profit of 250,000.

Solution Steps

The total cost \( C \) can be calculated using the formula: \[ C = F + (V \times Q) \] where:

• \( F \) is the fixed costs,
• \( V \) is the variable cost per unit,
• \( Q \) is the sales volume.

Substituting the given values: \[ C = 50000 + (20 \times 10000) \]

The total revenue \( R \) required to achieve the desired profit can be calculated as: \[ R = C + P \] where:

• \( P \) is the desired profit.

Substituting the total cost from Step 1 and the desired profit: \[ R = C + 250000 \]

The unit selling price \( P_u \) can be determined by dividing the total revenue by the sales volume: \[ P_u = \frac{R}{Q} \]

Substituting the total revenue from Step 2: \[ P_u = \frac{R}{10000} \]

After performing the calculations, we find that the unit selling price required to achieve an annual profit of $250,000 is \( 50.00 \).

Final Answer