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
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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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)
Rx = 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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