Question

It costs you c dollars each to manufacture and distribute backpacks. if the backpacks sell at x dollars each, the number sold is given by

n = a/x-c + b(100 -x) where a and b are certain positive constants. What selling price will bring a maximum profit?

Answer 1

To find the profit maximizing quantity for Doggies Paradise Inc., total revenue, marginal revenue, total cost, and marginal cost calculations show that the maximum profit of $40 is achieved at an output level of 5 units. This is the level where marginal cost equals marginal revenue.

Step-by-step explanation:

To determine the profit maximizing quantity for Doggies Paradise Inc., we need to calculate the total revenue, marginal revenue, total cost, and marginal cost for each level of output from one to five units. With the selling price at $72 per unit and the given variable costs, we construct a table:

• For unit 1: Total revenue = $72, Total cost = $100 (fixed) + $64 (variable) = $164, therefore, Marginal cost (MC) is not applicable for the first unit as there's no previous data point.
• For unit 2: Total revenue = $72 * 2, Total cost = $100 + $84, and MC = ($100 + $84) - ($100 + $64).
• The process is repeated up to unit 5.

By plotting these values on the diagrams, we see that the profit-maximizing quantity is where Marginal Cost (MC) equals Marginal Revenue (MR); this is the point where profit is maximized, and additional units would not increase profit any further.

Profit Maximization

Through comparison and the calculation of profits (Total Revenue - Total Cost) at each output level, we determine that the maximum profit occurs at the output where the gap between the total revenue and total cost is the greatest. In this case, the profit-maximizing output level is 5 units, with profits of $40. This is the point where the firm should stop increasing production, as producing more would lead to lower profits.