A software company produces a computer game. The company has determined that its profit P , in dollars, from the manufacture and sale of x games is given by where . How many games, to the nearest unit, does the company need to produce and sell to obtain the maximum profit?
A)5711 games
B)5756 games
C)5716 games
D)5706 games
E)5701 games

Question

A software company produces a computer game. The company has determined that its profit P , in dollars, from the manufacture and sale of x games is given by  where  . How many games, to the nearest unit, does the company need to produce and sell to obtain the maximum profit?
A)5711 games 
B)5756 games 
C)5716 games 
D)5706 games 
E)5701 games

Quizplus · Accepted Answer

To find the maximum profit, we need to find the vertex of the parabola given by the profit function. We can use the formula for the x-coordinate of the vertex:

x = -b/2a

In this case, a = -0.0044 and b = 98, so

x = -98/2(-0.0044) ≈ 5715.91

Rounding to the nearest unit, we get 5716 games as the answer. Therefore, the best choice is C.

A Software Company Produces a Computer Game