A company that produces video games estimates that the profit (in dollars) for selling a new game is given by where is the advertising expense (in tens of thousands of dollars).Using this model, how much should the company spend on advertising to obtain a profit of $6,500,000? Round to the nearest dollar.
A) $399,893 or $744,397
B) $433,844 or $721,190
C) $315,902 or $794,255
D) $368,914 or $764,017
E) $344,417 or $778,509

Question

A company that produces video games estimates that the profit  (in dollars) for selling a new game is given by   where  is the advertising expense (in tens of thousands of dollars).Using this model, how much should the company spend on advertising to obtain a profit of $6,500,000? Round to the nearest dollar.
A) $399,893 or $744,397 
B) $433,844 or $721,190 
C) $315,902 or $794,255 
D) $368,914 or $764,017 
E) $344,417 or $778,509

Quizplus · Accepted Answer

Setting the profit equation equal to $6,500,000 and solving for the advertising expense gives:

$6,500,000 = -70,000(x^2) + 5000x + 13,200

Using the quadratic formula gives:

x = (-5000 ± √(5000^2 - 4(-70,000)(13,200 - 6,500,000))) / (2(-70,000))

x ≈ 0.721 or x ≈ -0.433

Since the advertising expense must be positive, the company should spend approximately $721,190 on advertising to obtain a profit of $6,500,000. Therefore, the answer is B).

A Company That Produces Video Games Estimates That the Profit