1 . a shipping company handles rectangular boxes provided the sum of the height and the girth of the box does not exceed 96 in. ( the girth is the perimeter of the smallest base of the box). Find the dimensions of the box that meets this condition and ahs the largest volume using Lagrange Multipliers. Include a picture of the box with your labels. Show all the work involved in solving problem
2. use LAgrange multipliers to solve the following exercise
A home improvement contractor is apinting the walls and the ceilling of a rectangular room . The voulme of the room is 198.00 cubic ft. The cost of the wall is $ 0.06 per square foot and the cost of the ceilling paint is $ 0.11 per square foot.find the room dimensions that result in a minimum cost for the paint.
lenght ft?
width ft?
height ft?
what is the minimum cost for the paint? ( round your answer to two decimal places)