Calculus I Optimization

If y=2x-8, what is the minimum value of the product xy?

• -16

• -8

• -4

• 2

We want to construct a box whose base length is 3 times the base width. If the box must have a volume of 50 ft³, determine the dimensions that will minimize the amount of material used.

• w=2.027ft, h=4.055ft, l=6.082ft
• w=1.488ft, h=3.347ft, l=6.694ft
• w=2.231ft, h=3.347ft, l=6.694ft
• w=0.485ft, h=2.111ft, l=4.222ft

A rectangular  page is to contain 144 sq. inches of print. the margins on each side are 1 inch. Find the dimensions of the page that would use the least paper

• 16, 16
• 15,15
• 14,14
• 13,13

The volume of a cone of radius r and height h is given by v = (1/3) π r² h. If the radius and the height both increase at a constant rate of 1/2 centimeter per second, at what rate, in cubic centimeters per second, is the volume increasing when the height is 9 centimeters and the radius is 6 centimeters?

• 10π

• 24π

• 54π

• 108π

A water tank, shaped like an inverted circular cone, has a base radius of 6 ft and a height of 9 ft. The tank is completely full and needs to be drained. The valve is opened and the water begins to decrease at a rate of 2 ft³/sec.  How fast is the height of the water changing when the water is 2 ft deep?

• -9/(8pi) ft/sec
• 9/(8pi) ft/sec
• -8/(9pi) ft/sec
• 8/(9pi) f/tsec

A boat is being pulled into dock by means of a winch 12 feet above the deck of the boat.  Suppose the boat is moving at a constant rate of 4 feet per second.  Determine the speed at which the winch pulls in rope when there is a total of 13 feet of rope out.

• 2.32 ft/s
• -1.54 ft/s
• 12.2 ft/s
• -4.32 ft/s