Solve Problems Involving a Quadratic Function’s Minimum or Maximum Value

Question

Suppose that the price per unit in dollars of a cell phone production is modeled by p=50−0.0125x, where x is in thousands of phones produced, and the revenue represented by thousands of dollars is R=x*p. Find the production level that will maximize revenue.

Answer 1

p(x) = -0.0125x + 50

 

R(x) = xp(x) = -0.0125x² + 50x

 

R(x) is maximum at the vertex of the R(x)-vs.-x parabola, which is at

 

x = -50/[2(-0.0125)] = ?

 

Evaluate R(x) at this value of x to get the maximum R(x).  You can finish from here.