Question

4) A company that specializes in manufacturing reproductions of classic automobiles has fixed costs of $720,000 and variable costs of $35,000 per automobile. The automobiles sell for $50,000. a.) Write a function, C, for the cost of producing X automobiles. What is the cost of producing 60 automobiles? (5 points) b.) Write a function, R, for the revenue the company makes when selling x automobiles. (5 points) c.) Write a function, P, for the profit in terms of x. What value of x will be the break-even point? (10 points)

Answer 1

4a) Cost Function --> Cost of producing 'x' automobiles (C) = Fixed costs + (Variable cost per automobile x 'x') --> C = $720,000 + $35,000'x' 4b) Revenue Function --> Revenue from selling 'x' automobiles (R) = Selling price per automobile x 'x' --> R = $50,000'x' 4c) Profit Function --> P=R-C = $50,000'x' - $720,000 - $35,000'x' --> P = ($50,000 - $35,000)'x'- $720,000 --> P = $15,000'x'- $720,000 Breakeven point, in units is a sales volume at which firm's net income is zero. In simple words, firm's total revenue will be equal to total cost at its breakeven sales volume in units. It can be calculated by dividing firm's fixed costs by contribution margin per unit where the contribution margin per unit = Selling price per unit - Variable costs per unit. It is calculated as $15,000 in the profit function already. So, Fixed costs Contribution margin per unit Number of automobiles to sell to reach break-even $720,000 $15,000 ($50,000 - $35,000] 48 $720000 / $15000] Alternatively, Breakeven sales volume, in units can be calculated by equating firm's profit function to $0 because profit will be zero at breakevent sales. $0 = $15,000'x' - $720,000 $15,000'x' = $720,000 x' = $720,000/$15,000 'x'= 48