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PROBLEMS 1. The highway department is planning to build a picnic park for motorists along a major highway. The park is to be rectangular with an area of 5000 sq. yards and is to be fenced off on the three sides not adjacent to the highway. What is the least amount of fencing required for this job? How long and wide should the park be, for the fencing to be minimized? 2. A cable is to be run from a power plant on one side of a river 900 meters wide to a factory on the other side, 3000 meters downstream. The cost of running the cable under the water is Php500.00/meter, while the cost over land is Php 400.00/meter. What is the most economical route over which to run the cable? 3. A rectangle is inscribed in a right triangle, 5 by 12 by 13 units. What are the dimensions of the A closed box with a square base is to have a volume of 250 cu in. The material for the top and bottom of the box costs Php 2/sq in and the material for the sides costs Php 1/sq in. Can the box be constructed for Php 300.00? 4. A car travelling north at 60 mph and a truck travelling east at 45 mph leave an intersection at the same time. At what rate is the distance between them changing 2 hours later? 5. Water is running out of a conical funnel at the rate of 1000 cu mm/sec. If the radius of the funnel is 40 mm and the altitude is 80 mm, find the rate at which the water is dropping when it is 20 mm from the top. 6. Two parallel sides of a rectangle are being lengthened at the rate of 20 mm/sec, while the other two sides are shortened in such a way that the figure remains a rectangle with a constant area of 5000 sq mm. What is the rate of change of the perimeter P when the length of the increasing side is 50 mm. 7. An LRT train 6 meters above the ground crosses a street at a speed of 9 m/sec, at the instant that a car approaching at a speed of 4 m/sec is 12 meters up the street. Find the rate at which the LRT train and the car are separating two seconds later.

PROBLEMS
1. The highway department is planning to build a picnic park for motorists along a major highway. The park is to be rectangular with an area of 5000 sq. yards and is to be fenced off on the three sides not adjacent to the highway. What is the least amount of fencing required for this job? How long and wide should the park be, for the fencing to be minimized?
2. A cable is to be run from a power plant on one side of a river 900 meters wide to a factory on the other side, 3000 meters downstream. The cost of running the cable under the water is Php500.00/meter, while the cost over land is Php 400.00/meter. What is the most economical route over which to run the cable?
3. A rectangle is inscribed in a right triangle, 5 by 12 by 13 units. What are the dimensions of the A closed box with a square base is to have a volume of 250 cu in. The material for the top and bottom of the box costs Php 2/sq in and the material for the sides costs Php 1/sq in. Can the box be constructed for Php 300.00?
4. A car travelling north at 60 mph and a truck travelling east at 45 mph leave an intersection at the same time. At what rate is the distance between them changing 2 hours later?
5. Water is running out of a conical funnel at the rate of 1000 cu mm/sec. If the radius of the funnel is 40 mm and the altitude is 80 mm, find the rate at which the water is dropping when it is 20 mm from the top.
6. Two parallel sides of a rectangle are being lengthened at the rate of 20 mm/sec, while the other two sides are shortened in such a way that the figure remains a rectangle with a constant area of 5000 sq mm. What is the rate of change of the perimeter P when the length of the increasing side is 50 mm.
7. An LRT train 6 meters above the ground crosses a street at a speed of 9 m/sec, at the instant that a car approaching at a speed of 4 m/sec is 12 meters up the street. Find the rate at which the LRT train and the car are separating two seconds later.

Added by Jade A.

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