Explanation Given information: The function f ( x , y ) = 12 + 5 y − 20 x , and the polygon is shown in Figure 22(A) Concept Used: A linear function f ( x , y ) = a x + b y + c has no critical point, therefore the global maximum and minimum value of must occur on the boundary of a bounded domain Calculation: As f ( x , y ) = 12 + 5 y − 20 x is a linear function thus it has no critical point, therefore the global maximum and minimum value of must occur on the boundary of the polygon of Figure 22(A) As the polygon in figure 22(A) have boundary points ( − 3 , 0 ) , ( 1 , 0 ) , ( 0 , − 4 ) , ( 0 , 2 ) , checking value of function f ( x , y ) = 12 + 5 y − 20 x on boundary points f ( − 3 , 0 ) = 12 + 5 ( 0 )

4th Edition

ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

See similar textbooks

Concept explainers

Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calcul…

Videos

Question

Chapter 14.7, Problem 35E

To determine

Find the global maximum and global minimum value of f(x,y)=12+5y−20x on the specified polygon shown in Figure 22(A) and indicate where they occur

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.7, Problem 34E

Chapter 14.7, Problem 36E

Students have asked these similar questions

Consider the region below f(x) = (11-x), above the x-axis, and between x = 0 and x = 11. Let x; be the midpoint of the ith subinterval. Complete parts a. and b. below. a. Approximate the area of the region using eleven rectangles. Use the midpoints of each subinterval for the heights of the rectangles. The area is approximately square units. (Type an integer or decimal.)

Rama/Shutterstock.com Romaset/Shutterstock.com The power station has three different hydroelectric turbines, each with a known (and unique) power function that gives the amount of electric power generated as a function of the water flow arriving at the turbine. The incoming water can be apportioned in different volumes to each turbine, so the goal of this project is to determine how to distribute water among the turbines to give the maximum total energy production for any rate of flow. Using experimental evidence and Bernoulli's equation, the following quadratic models were determined for the power output of each turbine, along with the allowable flows of operation: 6 KW₁ = (-18.89 +0.1277Q1-4.08.10 Q) (170 - 1.6 · 10¯*Q) KW2 = (-24.51 +0.1358Q2-4.69-10 Q¹²) (170 — 1.6 · 10¯*Q) KW3 = (-27.02 +0.1380Q3 -3.84-10-5Q) (170 - 1.6-10-ºQ) where 250 Q1 <1110, 250 Q2 <1110, 250 <3 < 1225 Qi = flow through turbine i in cubic feet per second KW = power generated by turbine i in kilowatts

Hello! Please solve this practice problem step by step thanks!

Chapter 14 Solutions

Calculus: Early Transcendentals

Ch. 14.1 - Prob. 1PQ Ch. 14.1 - Prob. 2PQ Ch. 14.1 - Prob. 3PQ Ch. 14.1 - Prob. 4PQ Ch. 14.1 - Prob. 5PQ Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E Ch. 14.1 - Prob. 5E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Find the global maximum and global minimum value of f ( x , y ) = 12 + 5 y − 20 x on the specified polygon shown in Figure 22(A) and indicate where they occur

Solution Summary: The author explains that the global maximum and minimum value of f(x,y)=12+5y-20x must occur on the boundary of a bounded domain.

Concept explainers

Videos

Find the global maximum and global minimum value of f(x,y)=12+5y−20x on the specified polygon shown in Figure 22(A) and indicate where they occur

Want to see the full answer?

Chapter 14 Solutions