Question

You are the manager of Sassy Suf Creatons, a new trend-etting clethng manutacturer. The cost fuoctica for your very exclussve Tal Kwon Do Dragon T shirts is C-0.05 per week 50x+0 dolars per week, where ris the amber of ahirts you maratacture per week, up to a maxiaua of 30 sirts minmize the average cost? (Recal thet the average cost is given by Cuo- How many shirta per week vou ahould marutacture in order t You said above that the key is to set up the problem so that it amounts to locating the absolute maximum er minimum of a certain "objective function. What is the abjective function r this problem? st function C To detemine the objective functicn in any optimizaticn problem, ak yourself: "The problem acks us to find the maximum r minimum) what?" Here, the problem asks us to find the minimum average cost, so the objective function is the averaze a ,05z-50+ Check Clear Hint Objective function: Average cost Cz-005x+50+80x avarage cont function Tha graph wll anpaar if you correctly onter 10 20 3 50 60 70 50 で- 120-80x2 Check Clear Hint Check Clear I Left end-point of domain: -dne dne Accurats to two decmal places Enter dne for beth coordinates if there is no left endpoint Check ClearHint Right end-point of domain: Accurate to two deomal places Enter dne for both coordinatas if there is no right endpoint Check Clear Hint Stationary point: z Accurate to two deomal places Conclusion: shts per week et a minimum average daily cost of$ Check Clear Manufacture per shit

Answer 1

We dave, + Average Cast C 0'0 Sχ+ 0XH86 Say 86 S0.0 (02)(0),2 20 160 a minimum Valhe. () as Partting )0, L 20 1 1600=4υ". ζ χ 20 : x = 40 40 Shirst shoald he menafectured per 50, e k to mininize the average east