Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
A small company produces three types of goods. The profit function is given by P(x, y, z) = 5 ln(x + 1) + 8 ln(y + 1) + 12 ln(z + 1), where x, y and z are the monthly quantities sold of goods of type 1, 2 and 3, respectively. The production cost per unit of type 1 goods is $ 10; the cost per unit of type 2 goods is $ 15; the cost per unit of type 3 goods is $ 30. The monthly budget of the company (which is spent entirely on the 3 types of goods) is $2945. How should the budget be allocated to maximize the monthly profit? ● ● You do not need to investigate boundary points and it suffices to find a relative maximum. You might want to work with the variables x = x + 1, y = y + 1 and z = z + 1 to make the calculations easier.

A small company produces three types of goods. The profit function is given by P(x, y, z) = 5 ln(x + 1) + 8 ln(y + 1) + 12 ln(z + 1), where x, y and z are the monthly quantities sold of goods of type 1, 2 and 3, respectively. The production cost per unit of type 1 goods is $ 10; the cost per unit of type 2 goods is $ 15; the cost per unit of type 3 goods is $ 30. The monthly budget of the company (which is spent entirely on the 3 types of goods) is $2945. How should the budget be allocated to maximize the monthly profit? ● ● You do not need to investigate boundary points and it suffices to find a relative maximum. You might want to work with the variables x = x + 1, y = y + 1 and z = z + 1 to make the calculations easier.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
100%
A small company produces three types of goods. The profit function is given by P(x, y, z) = 5 ln(x + 1) + 8 ln(y + 1) + 12 ln(z + 1), where x, y and z are the monthly quantities sold of goods of type 1, 2 and 3, respectively. The production cost per unit of type 1 goods is $ 10; the cost per unit of type 2 goods is $ 15; the cost per unit of type 3 goods is $ 30. The monthly budget of the company (which is spent entirely on the 3 types of goods) is $2945. How should the budget be allocated to maximize the monthly profit? You do not need to investigate boundary points and it suffices to find a relative maximum. You might want to work with the variables x = x + 1, y = y + 1 and z = z + 1 to make the calculations easier.
Transcribed Image Text:A small company produces three types of goods. The profit function is given by P(x, y, z) = 5 ln(x + 1) + 8 ln(y + 1) + 12 ln(z + 1), where x, y and z are the monthly quantities sold of goods of type 1, 2 and 3, respectively. The production cost per unit of type 1 goods is $ 10; the cost per unit of type 2 goods is $ 15; the cost per unit of type 3 goods is $ 30. The monthly budget of the company (which is spent entirely on the 3 types of goods) is $2945. How should the budget be allocated to maximize the monthly profit? You do not need to investigate boundary points and it suffices to find a relative maximum. You might want to work with the variables x = x + 1, y = y + 1 and z = z + 1 to make the calculations easier.
Expert Solution
steps

Step by step

Solved in 5 steps with 23 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS