Question

A video game development company has created a new game and needs to decide how much to sell the game for in stores. The company's accountants created a function to represent the total expected profit, P, from selling each copy of the game at a price of x dollars. The graph of the function is shown below.

A negative quadratic function is plotted on a coordinate plane with y-axis labeled P and x-axis labeled x. The graph intercepts the y-axis at negative 800 thousand. The graph intercepts the x-axis at about (4, 0) and at about (62, 0). There is a maximum at approximately (33, 2.6 million). The graph also passes through the following points. (11, 1 million), (20, 2 million), (23, 2.2 million), (44, 2.2 million), (47, 2 million), (56, 1 million), and (68, negative 1 million).

Based on this profit function, which statement is true?

A.
The company can expect the greatest profit if it prices the game at $62 per copy.

B.
The company will not sell any copies of the game if the price is below $4 per copy.

C.
The company can earn a maximum of about $33 million in profit from selling the new game.

D.
The company will earn at least $2 million in profit if it prices the game between $20 and $47 per copy.

Answer 1

D

Explanation: The graph has a maximum profit of about $2.6 million at $33. At x = 20 and x = 47 the profit is about $2 million, and between those prices the quadratic stays at or above $2 million. The other choices are incorrect (profit at $62 is 0, prices below $4 give negative profit, and the maximum profit is about $2.6 million, not $33 million).