Chapter 4.2, Problem 32PPSE

Solution

To find: The maximum revenue from a sell modeled as a quadratic function of price

The maximum revenue is $ 25000 when the price per unit of software is $100.

Given data:

The model for company’s sale revenue R as the quadratic function of the price p is $R\left(p\right)\text{=-2}\text{.5}{p}^{\text{2}}+500p$ .

Method/Formula used:

The graph of a quadratic function is always a parabola. The y - coordinate of the vertex of is the (i) maximum value of the function if parabola opens down, and (ii) minimum if the parabola opens up. Using graphing facility the maximum or minimum value can be obtained.

Graph: The graph of revenue function is shown in Fig. (1).

The company’s sale revenue R as the quadratic function of the software price p is

  $R\left(p\right)\text{=-2}\text{.5}{p}^{\text{2}}+500p$ … (1)