To find: the minimum and maximum values of the given objective function and the points where the values occur.
Answer to Problem 29E
The minimum value of
The maximum value of
Explanation of Solution
Given:
The given objective function
Constraints:
Calculation:
Objective function
Subjected to the following constraints:
The area bounded by the constrains is as shown below:
Now, to find the co-ordinates of the point where the two lines intersect. The lines are:
From equation (1)
From equation (2)
At the intersection point
Substituting this value in equation (3), we get the value
So the co-ordinates of the intersection point is
At the four vertices of the region formed by the constraints the objective function has the following values:
At
At
At
At
So, the maximum value of
The minimum value of
Chapter 7 Solutions
EBK PRECALCULUS W/LIMITS
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning