1.A rectangular field adjacent to a river is to be enclosed. Fencing along the river costs Php 350 per meter, and the fencing for the other side costs Php 200 per meter. The area of the field is to be 1200 square meters. Find the dimensions of the field that is the least expensive to enclose

2.A 4-meter length of stiff wire is cut in two pieces. One piece is bent into the shape of a square and the other into a rectangle whose length is 3 times its width. Find the largest sum of the area that can be made this way.

3.A power line is needed to connect a power station on the shore of a river to an island 4 miles downstream and 1 mile offshore. Find the minimum cost for such a line given that is costs PhP 2,500,000.00 per mile to lay wire under the water and PhP 1,500,000.00 per mile to lay wire underground.

4.Find the largest circular cylinder that can be inscribed in a circular cone of height 6 feet and radius 2 feet.

5.A meteor (spherical in shape) enters earth's atmosphere and starts burning up in such a way that its surface area decreases at a constant rate of 100 cm2/s. Find the rate at which the diameter is changing when the radius is 5 m.

6.Budek is flying a kite. The kite is initially directly over her head at a height of 30 m. Then the wind starts carrying the kite in one direction at a rate of 40 m/min while Zoe starts running in the opposite direction at a rate of 200 m/min. Assuming that the height of the kite remains constant and that the string forms a straight line, find the rate at which the string is paying out after 10 s.

7.The ice cream in a sugar cone (conically shaped) has all melted and is dripping out a hole in the bottom of the cone at a constant rate of 2 cm3/min. Assuming that the cone is 12 cm tall and has a radius at the top of 4 cm, find the rate at which the level of the melted ice cream is dropping when the level is 3 cm.

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