a.
The table whose perimeter is 2400 and area of each configuration is maximum.
a.
Answer to Problem 21P
The possible pairs whose perimeter is 2400 and area is maximum is length =1200 and breadth=600.
Explanation of Solution
Given information:
Concept Used:
Let x is the breadth of rectangular field and y is the length of rectangular field.
Then
y is the side parallel to river and x is the other side.
Calculation:
X | Y | Product |
100 | 2200 | 210000 |
200 | 2000 | 40000 |
300 | 1800 | 540000 |
400 | 1600 | 640000 |
500 | 1400 | 700000 |
600 | 1200 | 720000 |
700 | 1000 | 700000 |
Conclusion:
Only these values are possible after that area start decreasing. So answer for maximum area 600 is breadth and 1200 is length.
b.
To determine the area in terms of one side.
b.
Answer to Problem 21P
The area is
Explanation of Solution
Given information :
Perimeter is
Concept Used:
Perimeter is
Let length of rectangular field be y and breadth be x.
Calculation:
Fencing along three sides of river.
Put equation 2 in 1,
Conclusion:
The required area in terms of one side is
c.
To compare the answer with subpart a .
c.
Answer to Problem 21P
The answer is same as subpart a .
Explanation of Solution
Given information :
Perimeter is
Concept used:
Maximise the area by using differentiation.
First differentiation is equal to zero for maximization.
Calculation:
Differentiate with respect to x ,
Put
Conclusion:
The answer is same as subpart a . So model of function is correct.
Chapter 2 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
- 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