The total revenue (in hundreds of dollars) from the sale of x spas and y solar heaters is approximated by R(x,y) = 19 + 162x + 210y - 3x2 - 5y? - 6xy. Find the number of each that should be sold to produce maximum revenue. Find the maximum revenue. Find the derivatives Ryx, Ry, and Ryy- R = Rw = Ryy

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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The total revenue (in hundreds of dollars) from the sale of x spas and y solar heaters is approximated by R(x,y) = 19+ 162x + 210y – 3x² – 5y2 - 6xy. Find the number of each that should be sold to produce
maximum revenue. Find the maximum revenue.
Find the derivatives Rxx, Ryy, and Rxy.
Rx =, Ry =D, Ry =]
%3D
%3D
Transcribed Image Text:The total revenue (in hundreds of dollars) from the sale of x spas and y solar heaters is approximated by R(x,y) = 19+ 162x + 210y – 3x² – 5y2 - 6xy. Find the number of each that should be sold to produce maximum revenue. Find the maximum revenue. Find the derivatives Rxx, Ryy, and Rxy. Rx =, Ry =D, Ry =] %3D %3D
Expert Solution
Step 1

Revenue function is given

R(x,y) = 19+162x+210y-3x2-5y2-6xy  , it is function of two variable 

Finding the partial derivative of R(x,y), differentiating with respect to x 

Rx = ϐ/ϐx(R) = ϐ/ϐx(19+162x+210y-3x2-5y2-6xy)

R= 0+162+0-6x-0-6y

Rx = -6x-6y+162 ....(1) ,differentiating again equation(1)

Rxx = ϐ/ϐx(-6x-6y+162)

Rxx = -6

Differentiating R with respest to y

Ry = ϐ/ϐy(19+162x+210y-3x2-5y2-6xy)

Ry = 0+0+210-0-10y-6x

Ry = 210-10y-6x  ....(2) , differentiating again

Ryy = ϐ/ϐy(210-10y-6x)

Ryy = -10

Differentiating equation (1) with respect y

Rxy = ϐ/ϐy(6x-6y+162)

Rxy = -6

 

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