If the area of the garden is 1000 square feet, Find the dimensions of the garden that minimize the cost.
Car B is 30 miles directly east of Car A and begins moving west at 90 mph. At the same moment car A begins moving north at 60 mph. What will be the minimum distance between the cars and at what time t does the minimum distance occur ?
Assume that the two cars travel at the following rates :
On
the same side of a straight river are two towns, and the towns people want to
build a pumping station, S, that supplies water to them. The pumping station is
to be at the river’s edge with pipes extending straight to the two towns. The
distance is shown in the figure beside. Where should the pumping station be
located to minimize the total length of pipe?
2. Build a rectangular pen with three parallel partitions using 500 feet of fencing. What dimensions will maximize the total area of the pen ?
Answer: The largest possible area of the pen is 6,250 ft.2
1. An open rectangular box with square base is to be made from 48 ft. 2 of material. What dimensions will result in a box with the largest possible volume?
A sheet of cardboard 3ft by 4ft will be made into a box by cutting equal-sized squares from each corner and folding up the four edges. What will be the dimensions of the box with the largest volume?
Answer:
The dimensions of the box in the largest volume has the volume of 3.03 ft^3.
Optimization Problem Example
Find the dimensions of a rectangle with area 1000 m ^ 2, whose perimeter is as small as possible.
ANSWER:
