Find the maximum area.
10. Area Find the dimensions of the rectangular field of maximum area that can be made from 300 m of fencing material. (This fence has four sides.)
11. Area An ecologist is conducting a research project on breeding pheasants in captivity. She first must construct suitable pens. She wants a rectangular area with two additional fences across its width, as shown in the sketch. Find the maximum area she can enclose with 3600 m of fencing.
12. Area A farmer is constructing a rectangular pen with one additional fence across its width. Find the maximum area that can be enclosed with 2400 m of fencing.
13. Cost with Fixed Area A fence must be built in a large field to enclose a rectangular area of 25,600 m". One side of the area is bounded by an existing fence; no fence is needed there. Material for the fence costs $3 per meter for the two ends and $1.50 per meter for the side opposite the existing fence. Find the cost of the least expensive fence.
14. Cost with Fixed Area A fence must be built to enclose a rectangular area of 20,000 ft". Fencing material costs $2.50 per foot for the two sides facing north and south and $3.20 per foot for the other two sides. Find the cost of the least expensive fence.
15. Revenue A local club is arranging a charter flight to Hawaii. The cost of the trip is $1600 each for 90 passengers, with a refund of $10 per passenger for each passenger in excess of 90.
(a) Find the number of passengers that will maximize the revenue received from the flight.
(b) Find the maximum revenue.