Question

4. A rancher with 300 ft of fence intends to enclose a rectangular corral, dividing it in half by a fence 5. A rectangular garden of area 75 ft2 is bounded on three sides by a wall costing $8 per ft and on the 6. An open box is made from a 16 x 16 cm piece of cardboard by cutting equal squares from each corner parallel to the short sides of the corral. How much area can be enclosed? fourth by a fence costing $4 per ft. What are the most economical dimensions of the garden? and folding up the sides. For maximum volume, what size squares should be cut out?

Answer 1

To maximize a function f(x) 1st we need to find its critical numbers

For critical numbers we need to put differentiation of f(x) zero i.e. f '(x) = 0

Then check second derivative of f(x) i.e. f ''(x) is positive or negative at critical numbers If f ''(x) >0 then that gives minimum value of f(x) and if f ''(x) <0 then that give maximum value of f(x) .

21 be. dn ord Jonepox Correl divided in haar by bere e Parallel マイブャ.3n--3U

2 27 一 石-

5/ S- ora bseceh 71 十16n. el.

4 3 シー-- crini cal par sm -3

hope y n Salre l6 6 m volume v