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2. According to the US Postal Service, a rectangular box is classified as "oversized" if its height plus the perimeter of its base is more than 108 inches. In this problem, you will find the dimensions of a box that has a square base and the largest possible volume without being oversized. (a) Identify some variables: (Remember the box should have a square base.) (b) (Given) Since you want the box to be as large as possi- ble, without being oversized, the height of the box plus the perimeter of its base should be exactly as large as possible... meaning exactly 108 inches. Write this as an equation. (This is called a constraint.) (c) (Find) In terms of your variables, what quantity are you trying to maximize? (d) (Equation) Solve your constraint equation (from part (b)) for one variable, and substitute this into the expression from part (c) to get a function that's in terms of just one variable. This is the function you want to maximize. (e) (Solve) Maximize the function you found. (Be sure to verify that your solution is indeed a maximum, by using either the number line test or the second derivative test.)

          2. According to the US Postal Service, a rectangular box is classified as "oversized" if its
height plus the perimeter of its base is more than 108 inches. In this problem, you will
find the dimensions of a box that has a square base and the largest possible volume
without being oversized.
(a) Identify some variables: (Remember the box should have a square base.)
(b) (Given) Since you want the box to be as large as possi-
ble, without being oversized, the height of the box plus
the perimeter of its base should be exactly as large as
possible... meaning exactly 108 inches. Write this as an
equation. (This is called a constraint.)
(c) (Find) In terms of your variables, what quantity are you trying to maximize?
(d) (Equation) Solve your constraint equation (from part (b)) for one variable, and
substitute this into the expression from part (c) to get a function that's in terms
of just one variable. This is the function you want to maximize.
(e) (Solve) Maximize the function you found. (Be sure to verify that your solution is
indeed a maximum, by using either the number line test or the second derivative
test.)

2. According to the US Postal Service, a rectangular box is classified as "oversized" if its
height plus the perimeter of its base is more than 108 inches. In this problem, you will
find the dimensions of a box that has a square base and the largest possible volume
without being oversized.
(a) Identify some variables: (Remember the box should have a square base.)
(b) (Given) Since you want the box to be as large as possi-
ble, without being oversized, the height of the box plus
the perimeter of its base should be exactly as large as
possible... meaning exactly 108 inches. Write this as an
equation. (This is called a constraint.)
(c) (Find) In terms of your variables, what quantity are you trying to maximize?
(d) (Equation) Solve your constraint equation (from part (b)) for one variable, and
substitute this into the expression from part (c) to get a function that's in terms
of just one variable. This is the function you want to maximize.
(e) (Solve) Maximize the function you found. (Be sure to verify that your solution is
indeed a maximum, by using either the number line test or the second derivative
test.)

Added by Tara G.

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