Complete the following applied optimization word problem. Include a well-labeled figure, clearly defined objective function of one variable, interval for which that variable is logical and supporting...

 Complete the following applied optimization word problem. Include a well-labeled figure, clearly defined objective function of one variable, interval for which that variable is logical and supporting mathematical statements to justify that the optimal result is achieved for the function on the interval within a grammatically correct exposition.

To mail a package with the United States Postal service without additional fees, the sum of the length and the girth of the package must be less than or equal to 92 inches, where the length is the length of the longest side and the girth is the distance around the package perpendicular to its length. Suppose Tom wants to mail a box with a length of 48 inches. What is the largest possible surface area that Tom’s package can have? Make sure that the length of the package corresponds to the longest side.