   Chapter 7.5, Problem 38E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Revenue A retail outlet sells two types of riding lawn mowers, the prices of which are p 1  and  p 2 . Find p 1  and  p 2 so as to maximize total revenue, where R   = 870 p 1 + 950 p 2 +   1.5 p 1 p 2 − 1.5   p 1 2 − p 2 2 .

To determine

To calculate: The values of p1 and p2 to maximize the total revenue if the total revenue is provided by R=870p1+950p2+1.5p1p21.5p12p22, where p1 and p2 are prices of two types of riding lawn mowers.

Explanation

Given Information:

The total revenue is provided by R=870p1+950p2+1.5p1p21.5p12p22, where p1 and p2 are prices of two types of riding lawn mowers.

Formula used:

If the function y=f(x) has a maximum at a point then their first partial derivatives fx(x) and fy(x) at that point are zero.

Calculation:

Consider the total revenue,

R=870p1+950p2+1.5p1p21.5p12p22

Now, the first partial derivatives are,

Rp1=p1[870p1+950p2+1.5p1p21.5p12p22]=870+1.5p23p1=3(290+0.5p2p1)

And,

Rp2=p2[870p1+950p2+1.5p1p21.5p12p22]=950+1.5p12p2=2(475+0

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