APPLIED CALCULUS EXTRAS
Problems 12.3: continued
16. A kennel owner would like to design a set of dog runs that contain a total area of 640 sq. ft. The area will consist of 4 adjacent identical rectangular runs against the back wall of the building (no fence needed against building). The front of the fence (parallel to the building) must be made out of material that costs $12.50 per foot. The side and interior divider material costs $8 per foot. State animal regulations require that the runs be at least 4 feet wide in any direction. What dimensions will minimize the cost of the fencing?
17. A rectangular enclosure is divided into three equal sections by having two dividers inside the enclosure. 640 ft of fencing is provided for this project. What dimensions will maximize the enclosed area?
18. A farmer has 1200 meters of fence with which he would like to enclose a rectangular field along a river. There is no fence needed along the river and the field must be at least 5 meters wide in each direction. What are the dimensions of the field that will maximize the enclosed area? What is that maximum area?
19. A rectangular field is to be enclosed on all four sides with a fence. Fencing material costs $3 per foot for two opposite sides and $6 per foot for the other two sides. The budget limit for fencing material is $2400. What are the fence dimensions that will maximize the enclosed area?
20. A farmer needs to enclose a rectangular pigpen with a fence. One side of the area is against a barn, so no fence is needed, and the pigs need at least 10 feet of length on any side in order to be able to move around. If material for the fence costs $2 per foot for the two ends and $4 per foot for the side parallel to the barn, find the dimensions of the pigpen of largest area that can be enclosed for a cost of $1000.