   Chapter 2.1, Problem 59E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

Explain why, if demand is a linear function of unit price p (with negative slope), then there must be a single value of p that results in the maximum revenue.

To determine

The reason, there must be a single value of unit price p (with negative slope) that results in maximum revenue, if demand is a linear function of unit price p.

Explanation

Given Information:

Demand is a linear function of unit price p.

The quadratic models are also used to solve demand revenue problems and there is only one single value that results in maximum value. That point corresponds to the vertex of the parabola on the graph.

For example:

Consider the given demand equation,

q=0.5p+140

The relationship between Revenue and Price is,

Revenue=(Price)(Demand)R(p)=(p)(q)

Substitute 0.5p+140 for q in Revenue equation:

R(p)=(p)(q)=p(0.5p+140)=0.5p2+140p

Therefore, the total Revenue R as a function of the price p per item for the given demand equation is R(p)=0.5p2+140p.

Consider the given annual income equation,

R(p)=0.5p2+140p

Compare the equation R(p)=0.5p2+140p with the standard function f(x)=ax2+bx+c and find the value of a,b and c.

The values are a=0.5,b=140 and c=0

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