The price of a product affects a company's revenue in two conflicting ways. First, when the product has a higher price, the company's revenue per product is higher. Second, however, when the product has a higher price, fewer people can afford to purchase it.

Question

Based on market research, a company finds that the following equation describes the relationship between x, the price of their product in dollars, and y, their annual revenue in millions of dollars.
y = -0.13x²+2.99x
Based on this equation, what is the company's maximum revenue, and what price should they set for their product to obtain this revenue? (Answer choices are rounded appropriately.)
The maximum revenue is $176.92 million. The company will obtain this revenue by charging $23.00 per product.
The maximum revenue is $2.99 million. The company will obtain this revenue by charging $0.13 per product.
The maximum revenue is $0.13 million. The company will obtain this revenue by charging $2.99 per product.
The maximum revenue is $17.19 million. The company will obtain this revenue by charging $11.50 per product.
The maximum revenue is $11.50 million. The company will obtain this revenue by charging $17.19 per product.

Answer 1

The correct answer is:
The maximum revenue is $17.19 million. The company will obtain this revenue by charging $11.50 per product.

This can be determined by finding the vertex of the quadratic equation y = -0.13x²+2.99x. The x-coordinate of the vertex is the price that will maximize revenue, and the y-coordinate of the vertex is the maximum revenue. The equation gives a maximum revenue of $17.19 million at a price of $11.50 per product.