Question

Steven owns a model airplane manufacturing business. Steven wants to maximize his revenue. He starts with the linear function x = -40p + 1600, where x is the predicted number of model airplanes he will sell at p dollars per airplane.

Based on this model, what is the maximum revenue in dollars that Steven would make selling his model airplanes? $_____

Answer 1

$16,000

Explanation:

Revenue is the product of price and the number sold. Using the given relation for number sold, the revenue as a function of price is ...

R(p) = p(-40p +1600) = -40p(p -40)

This is the equation of a quadratic that opens downward and has zeros at p=0 and p=40. The vertex is halfway between those zeros, at p=20. The revenue at this price is ...

R(20) = -40·20(20 -40) = 16,000 . . . . dollars