a.
Write a function for the total area A of the page in terms of x .
a.

Answer to Problem 72E
A=2x(x+11)x−4
Explanation of Solution
Calculation:
Here, we will consider the figure given below:
As, the area of a rectangle is the product of length and width, the total area of the page is,
A=xy
Thus, the area of a print is:
(x−4)(y−2)=30y−2=30x−4y=2+30x−4y=2x+22x−4
Hence, the total area in terms of x is:
A=xyA=x(2x+22x−4)A=2x(x+11)x−4
b.
Find the domain of the function based on the physical constraints of the problem.
b.

Answer to Problem 72E
(4,∞)
Explanation of Solution
Calculation:
Here, since the margins on the left and right are 2 inches each, the width of the page x should be greater than4.
Hence, the domain is (4,∞) .
c.
Graph the area function and approximate the dimensions of the page by using graphing utility.
c.

Answer to Problem 72E
x≈12inches;y≈6inches
Explanation of Solution
Calculation:
Here, by using graphing utility the graph of the area function will be:
Now, by using trace utility it is found that the area is minimum when:
x≈11.75inchesy≈2(11.75)+2211.75−4y≈45.57.75y≈5.87inches
Hence, the area is minimum when x≈12inches;y≈6inches .
Chapter 2 Solutions
EBK PRECALCULUS W/LIMITS
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