A rectangular hole is to be cut in a wall for a vent. If the perimeter of the hole is 184 in. and the length of the diagonal is aminimum, what are the dimensions of thehole?

Let the length and width of the hole be x andy, respectively, and let the length of the diagonal be D. Find an equation that describes the quantity to be minimized

A box with a lid is to be made from a rectangular piece of cardboard measuring 30 cm by 90 cm. Two equal squares of side x are to be removed from oneend, and two equal rectangles are to be removed from the other end so that the tabs can be folded to form a box with a lid. Find x such that the volume of the box is a maximum.

x=_____cm

A company projects that its total savings S(in dollars) by converting to asolar-heating system with asolar-collector area A(in m2) will be equal to the formula below. Find the area that should give the maximum savings and find the amount of the maximum savings.

S=360A-0.05A³

m²=_______ (Round to the nearest square meter asneeded.)