l n 1 I o o - 2fM in the discussmn of economic lot srze, use the critical pornt theorem to show that IT is the economic lot size that minimizes total A v production costs. Critical Point Theorem Suppose a function f is continuous on an interval | and that f has exactly one critical number in the interval l. located at x = c. lff has a relative maximum at x = c, then this relative maximum is the absolute maximum off on the interval I. If f has a relative minimum at x= c. then this relative minimum is the absolute minimum of f on the interval l. T(q) is the total cost of producing M units in batches of size q. _f_~1+ We To nd the value of q that minimizes T(q). remember that f. g. k, and M are constant and nd T'(q). T'tq)=El Find the critical values of T(q) by setting TIM) q=l:l This is a critical point on the interval ( equal to 0 and solving for q. 0,00). Does this point minimize or maximize T(q)? O maximize O minimize