Question

What is the ideal selling price for a king-size sheet set that includes a luxurious reusable box, given a 50 percent margin on sales, total fixed costs of $540,000, and an estimated first-year sales volume of 30,000 sets, when the variable cost is $X and the cost per unit is $Y?

Answer 1

The profit-maximizing quantity for AAA Aquarium Co. is determined by comparing total revenue with total cost, and marginal revenue with marginal cost. The analysis shows that the company maximizes profit at four units where MR equals MC, and MR is above MC for all previous units of output.

Step-by-step explanation:

Profit Maximizing Quantity Calculation

The profit-maximizing quantity for AAA Aquarium Co. can be calculated by comparing total revenue (TR) and total cost (TC), as well as examining the relationship between marginal revenue (MR) and marginal cost (MC). The profit-maximizing output is found where MR equals MC, provided that MR exceeds MC for all previous units of output.

Below is the table and analysis for each output level (one to five units).

Three units: TR = $60, TC = $55, MR = TR = $20, MC = $10

Five units: TR = $100, TC = $100, MR = TR = $20, MC = $30

To determine the profit-maximizing quantity, we look at the point where MR equals MC, which occurs after the fourth unit. However, we need to ensure that for all previous outputs, MR is above MC. Since this condition is met for the first four units, the profit-maximizing quantity for AAA Aquarium Co. is four units.

Illustrative diagrams would show that the TR curve has a linear positive slope, indicating constant MR, while the TC curve starts at the fixed cost level and increases with output. The MR and MC curves intersect at the profit-maximizing output level, indicating that the company should increase production as long as MR exceeds MC.