Calculating Break-Even Production Quantity

A company is evaluating the profitability of two different plans for launching a new product. The first plan involves a fixed cost of $12,000, and the variable cost per unit produced is $50. The second plan has a lower fixed cost of $8,000 but a variable cost of $70 per unit. Let x represent the number of units produced. Determine the value of x where both plans have the same total cost.

To find the solution, set the total costs of both plans equal to each other:

Plan 1: Total Cost = Fixed Cost + (Variable Cost x Units) = $12,000 + $50x

Plan 2: Total Cost = Fixed Cost + (Variable Cost x Units) = $8,000 + $70x

Find x such that:

$12,000 + 50x = 8,000 + 70x$