Question

H.W#5: Break-Even Chart A firm manufactures a product that sells for $15 per unit. Variable cost per unit is $5 and Fixed Cost per period is $1500. Capacity per period is 1000 units. a) Graph the Revenue and Cost functions. b) Find the number of units sold and the revenue amount (\$) at break-even point. What is the profit if only 500 units are sold? c) Repeat (a) Using Excel Software or Matlab in your solution and show the loss and profit regions and B.E.P

Answer 1

a) The break-even point for this firm occurs at 300 units, generating $4,500 in revenue.

b) At 500 units sold, the profit is $2,500.

c) The graph in Excel/Matlab indicates the break-even point at 300 units and illustrates the profit and loss regions accurately.

Step-by-step explanation:

a) To determine the break-even point, we first calculate the total cost and total revenue. Total cost = Fixed Cost + (Variable Cost * Number of Units). For this scenario, Total Cost = $1500 + ($5 * x). Total Revenue = Selling Price * Number of Units = $15 * x. Setting Total Cost equal to Total Revenue gives us the break-even point: $1500 + ($5 * x) = $15 * x. Solving for x, we find x = 300 units. Revenue at this point is $15 * 300 = $4,500.

b) If 500 units are sold, the total cost would be $1500 + ($5 * 500) = $4000, while revenue would be $15 * 500 = $7500. Profit is Revenue - Total Cost, so profit = $7500 - $4000 = $2500.

c) Using Excel/Matlab, the graph depicts the cost and revenue functions, showcasing the break-even point at 300 units where cost equals revenue. It delineates the profit zone beyond the break-even point and the loss region below it. This visual representation aids in understanding the firm's profitability concerning different sales quantities. The break-even analysis is vital for decision-making, indicating the minimum sales needed to cover costs and illustrating the potential profits beyond that threshold.