Question

Darlena has started taking photos at amateur dog racing events, later offering the photos for sale to the dog owners by email. The prices she has charged per photo at each of her first three events, and the corresponding number of photos sold and total revenue raised appear in the table below. Price per Photo $56 $52 $24 Number of Photos Sold 4 5 12 Revenue $224 $260 $288 Treating revenue as a function of the number of photos sold, a graph of the three data points is also shown. If she uses quadratic regression to fit a curve to the data, what number of photos are sold, and what price per photo will maximize her revenue?

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Answer 1

The cost per photo is maximized about $127.95

Answer 2

To maximize profit for Doggies Paradise Inc., we calculate total revenue, marginal revenue, total cost, and marginal cost for output levels of one to five units of dog coats. We then draw a diagram with total revenue and total cost curves and a separate diagram with marginal revenue and marginal cost curves to determine the point where the marginal revenue equals marginal cost, which indicates the profit maximizing quantity.

Step-by-step explanation:

To answer this Business question, we need to calculate the total revenue, marginal revenue, total cost, and marginal cost for Doggies Paradise Inc. for each output level from one to five units of dog coats. We also need to create a diagram to visualize the total revenue and total cost curves, as well as another diagram for the marginal revenue and marginal cost curves, to determine the profit maximizing quantity.

Let's start by creating the table with the relevant information:

• Fixed costs: $100 (irrespective of output level)
• Variable costs and total cost (variable + fixed costs) are calculated for each level of output.
• Total revenue is the number of units sold multiplied by the price per unit ($72).
• Marginal revenue is the additional revenue from selling one more unit which, in a perfectly competitive market, is equal to the price of the product as each additional unit sells at the market price.
• The marginal cost is the additional cost of producing one more unit, obtained by the change in total cost when the output is increased by one unit.

With this information, we can find the profit maximizing quantity by looking at the point where the marginal cost equals the marginal revenue, as producing beyond this point will not increase profits.

Now, let's perform the calculations and then draw the required diagrams based on the calculated data to visually understand the point of maximum profit.