Question

A company produces and sells a consumer product and is able to control the demand for the product by varying the selling price. The approximate relationship between price and demand is p=$5+4,800/D - 3,000/D², for D>0. where p is the price per unit in dollars and D is the demand per month. The company is seeking to maximize its profit. The fixed cost is $2,000 per month and the variable cost (v) is $35 per unit. a. What is the number of units that should be produced and sold each month to maximize profit?

Answer 1

To determine the profit-maximizing quantity for Doggies Paradise Inc., calculate total revenue, total cost, and marginal cost for each output level, and then graph the total revenue and total cost curves, as well as the marginal cost and marginal revenue curves. The point where total revenue is greatest above total cost, and where marginal cost equals marginal revenue, indicates the optimal number of units to produce.

Step-by-step explanation:

Finding the Profit Maximizing Quantity for Doggies Paradise Inc.

To find the number of units Doggies Paradise Inc. should produce to maximize profit, we need to analyze the relationship between total revenue, total cost, and marginal costs for each output level from one to five units. To do this, we will calculate these metrics and then graph them to find the profit-maximizing quantity.

First, calculate the total revenue (TR) by multiplying the selling price by the number of units sold. Next, find the total cost (TC) at each level by adding fixed costs to the variable costs, and calculate marginal cost (MC) as the change in total cost when an additional unit is produced. The total revenue (TR) at each level of output is determined by the fixed price of $72 per unit.

By plotting total revenue and total cost on a graph and looking for the point where total revenue exceeds total cost by the greatest amount, we can find the profit-maximizing quantity. Similarly, plotting marginal cost and marginal revenue, the profit maximization point is where MR = MC.

The table below summarizes the calculations and can be used to aid in graphing:

• Total Revenue (TR): The revenue from selling each unit at $72.
• Total Cost (TC): The sum of fixed and variable costs for each output level.
• Marginal Revenue (MR): The additional revenue from selling one more unit, which is $72 in a perfectly competitive market.
• Marginal Cost (MC): The additional cost incurred from producing one more unit.

The profit-maximizing quantity is at the output level where the difference between total revenue and total cost is the greatest and where marginal cost is equal to marginal revenue.