To find: The model for the cost of fencing of the garden and the dimensions of garden that minimize the cost of fencing.
Answer to Problem 73E
The model for the cost of fencing of the garden is equal to
Explanation of Solution
Given information:
A property owner wants to fence a garden plot adjacent to a road, as shown in figure. The fencing next to the road must be sturdier and cost
Calculation:
As given the area of the garden is
So, the breadth of the rectangular garden is equal to
The cost of the fence along the roadside is
Evaluate the function for the total cost for fencing of garden.
So, the function of the total cost of fencing the garden is given by
To graph a function
First press “ON” button on graphical calculator, press
The display will show the equation,
Now, press the
Figure (1)
As observed from the graph, the cost function has minimum value equal to
So, the length of the region is equal to
Therefore, the model for the cost of fencing of the garden is equal to
Chapter 3 Solutions
Precalculus: Mathematics for Calculus - 6th Edition