Question

Mandela Manufacturing produces a single product that sells for $140. Variable costs per unit equal $28. The company expects total fixed costs to be $56,000 for the next month at the projected sales level of 1200 units.

How many units must be sold to earn Operating Income of $120,400?

Answer 1

To find the profit-maximizing quantity, calculate the total revenue, marginal revenue, total cost, and marginal cost for each output level. The profit-maximizing quantity is 3 units, where marginal revenue equals marginal cost. Sketch the total revenue and total cost curves and the marginal revenue and marginal cost curves to visually understand the relationship between quantities and costs.

Step-by-step explanation:

To find the profit-maximizing quantity, we need to calculate the total revenue, marginal revenue, total cost, and marginal cost for each output level. Here's a table summarizing the calculations:

Output LevelTotal RevenueMarginal RevenueTotal CostMarginal Cost1202040402402065253602010035480201404051002018545

From the table, we can see that the profit-maximizing quantity is 3 units. This is because at this quantity, marginal revenue equals marginal cost, which maximizes profits. At any other quantity, either marginal revenue is greater than marginal cost (causing profits to increase) or marginal cost is greater than marginal revenue (causing profits to decrease).

Sketching the total revenue and total cost curves on one diagram, we can see that the total revenue curve starts at the origin and increases linearly, while the total cost curve starts at the fixed costs and increases at a steeper rate. On another diagram, sketching the marginal revenue and marginal cost curves, we can see that the marginal revenue curve is constant at $20 (the price of each unit), while the marginal cost curve starts at $40 (the fixed costs) and increases at a steeper rate.