Question Help A rectangular page is to contain 12 square inches of and y. In thi

Question

Question Help A rectangular page is to contain 12 square inches of and y. In this problem, the print. The page has to have a 2-inch margin on top and that the printed area is fixed at 12 in at the bottom and a 6-inch margin on each side (see figure). Find the dimensions of the page that minimize Use the figure to the left to determine the constraint the amount of paper used. constraint equation is 2 equation. 12-xy The above equation yields x as a function of y L6 ky 61 12 12 12 Substitute the above expression into the objective equation in order to get it in terms of the variable y alone. A(y) = (y+12)( A() (y+12)4 4) 144 -60 + 4y+ y Since y represents a measure of distance, it must be positive. Hence, the domain for A(y) is ys 0 Press Continue to see more.

Explanation / Answer

We have given rectangular page printed area xy=12 in2

Let rectangular page Area A(y)=(x+4)*(y+12) where width =(x+2+2) and length =y+6+6

plug x=12/y into A

A(y)=(12/y+4)*(y+12)

=12/y *y+12/y*12 +4y+48

=12+144/y+4y+48

A(y)=60+144/y+4y

to minimize the Area of page we set A'(y)=0

A'(y)=0-144/y^2+4=0

-144/y^2+4=0

-144/y^2=-4

-4y^2=-144

y^2=144/4

y^2=(12/2)^2

y=12/2=6

plug y=6 into x=12/y

x=12/6=2

The dimensions of the rectangular page that is used as

width=x+2+2=2+2+2=6 since x=2

length =y+6+6=6+6+6=18 since y=6

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.