Complete Solution to §8-3 #10

[Things that you could omit without penalty are enclosed in square brackets.]

[Constraint:]




[Other] constraints:




[Obj. fcn.:] Area = A(r) =

Min. A(r) s.t.

Find crit. pts.:







Since the only possible crit. pt. has r out of domain, min. must occur at an endpt.

Check endpts.:





r = 20 gives
Answer: Use straight sections of 137.168m and curved sections w/ [inner radius] r = 20m.


[Note that it is not necessary to show work in computing A(20) and , since those are merely function evaluations.]

[Alternate approach: Instead of checking both endpoints, state that for all r in domain. Then state that the global min. must occur at the left endpoint.]