Fencing costs $4 per foot for two opposite sides ... It costs $6 per year to store a bag of potting soil, and it costs $. 1000 to set up the facility ...
Name___________________________________ Find the location of the indicated absolute extremum for Solve the problem. the function. 5) A rectangular field is to be enclosed on four 1) Minimum sides with a fence. Fencing costs $4 per foot for two opposite sides, and $2 per foot for the f(x) other two sides. Find the dimensions of the 5 field of area 600 ft2 that would be the cheapest 4 to enclose.
3 2 1 -5
-4
-3
-2
-1
1
2
3
4
x
5
-1 -2 -3 -4 -5
6) Find the dimensions that produce the maximum floor area for a one -story house that is rectangular in shape and has a perimeter of 127 ft.
2) Maximum g(x) 5 4 3 2 1 -5
-4
-3
-2
-1
1
2
3
4
5
x
-1 -2 -3
7) A piece of molding 188 cm long is to be cut to form a rectangular picture frame. What dimensions will enclose the largest area?
-4 -5
Find the locations of all absolute extrema if they exist. 3) f(x) = -3x4 + 20x3 - 36x2 + 6
4) f(x) =
x-1 2 x + 3x + 5
1
8) A company wishes to manufacture a box with a volume of 52 cubic feet that is open on top and is twice as long as it is wide. Find the width of the box that can be produced using the minimum amount of material.
12) A local office supply store has an annual demand for 50,000 cases of photocopier paper per year. It costs $3 per year to store a case of photocopier paper, and it costs $50 to place an order. Find the optimum number of cases of photocopier paper per order.
13) Find the approximate number of batches (to the nearest whole number) of an item that should be produced annually if 150,000 units are to be made. It costs $2 to store a unit for one year, and it costs $520 to set up the factory to produce each batch.
9) Find the dimensions of the rectangular field of maximum area that can be made from 540 m of fencing material.
14) A bookstore has an annual demand for 74,000 copies of a best-selling book. It costs $.30 to store one copy for one year, and it costs $125 to place an order. Find the optimum number of copies per order.
10) S(x) = -x3 - 9x 2 + 165x + 1300, 5 ≤ x ≤ 20 is an approximation to the number of salmon swimming upstream to spawn, where x represents the water temperature in degrees Celsius. Find the temperature that produces the maximum number of salmon.
15) Find the approximate number of batches (to the nearest whole number) of an item that should be produced annually if 150,000 units are to be made. It costs $1 to store a unit for one year, and it costs $360 to set up the factory to produce each batch.
11) A certain company produces potting soil and sells it in 50 lb bags. Suppose that 300,000 bags are to be produced each year. It costs $6 per year to store a bag of potting soil, and it costs $ 1000 to set up the facility to produce a batch of bags. Find the number of bags per batch that should be produced.
x=3 No maximum Absolute maximum at x = 0; no absolute minima Absolute minimum at x = -2; absolute maximum at x = 4 17.3 ft @ $4 by 34.6 ft @ $2 31.75 ft × 31.75 ft 47 cm × 47 cm 3.6 ft 135 m by 135 m 5°C 10,000 1291 17 batches 7853 copies 14 batches
