SOLUTION: . In the United Parcel Services example at the beginning , the length plus girth of a package was restricted to 108 inches. Suppose a shipper uses rectangular boxes with square end

Question 1151022: . In the United Parcel Services example at the beginning , the length plus girth of a package was restricted to 108 inches. Suppose a shipper uses rectangular boxes with square ends made of a perforated material to provide ventilation, the shipper wants the total surface area to be as large as possible. Use x as the side of the square base and L as the length.
a) Write the expression for the area, A, in terms of L and x.
b) Express A(x) as a function of x alone.
c) What value of x maximizes A(x)? Prove this is a maximum.
d) What are the dimensions of the maximum-area box?

Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
If "restricted to" means equal to then the system of equations fits the description.

Substituting and simplifying gives .

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