1) Find two positive numbers such that their product is 192 and the sum of the
first plus three times the second is a minimum.
2) Find two positive numbers such that the sum of the first and
twice the second is 100 and their product is a maximum
3
4
3.
4.
5) A farmer has 2400 ft of fencing and wants to fence off a rectangular field that borders a straight river. He needs no fence along the river. What are the dimensions of the field that has the largest area?
6) Find the dimensions of the rectangle of largest area which can be inscribed in the closed region bounded by the x­axis, y­axis, and graph of y=8­x3 7)
(Surface area=Total area of all the faces)
8) A square piece of tin has 12 inches on a side. An open box is formed by cutting out equal square pieces at the corners and bending upward the projecting portions which remain.Find the maximum volume that can be obtained.