It is estimated that the cost of constructing an office building that is n floors high isC(n)= 3n^2+500n+842thousand dollars. How many floors should the building have in order to minimize the average cost per floor? (Remember, your answer must be a whole number.) ______ floors
If the cost per floor is C(n) = 3n^2 + 500n + 842 then the average cost per floor would be this function divided by the number of floors n: A(n) = (3n^2 + 500n + 842)/n A(n) = 3n + 500 + 842/n This is the function we want to minimize, so take it's derivative: A'(n) = 3 + 0 + -842/n^2 To find possible max/min values, set the derivative equal to zero: 0 = 3 - 842/n^2 842/n^2 = 3 842 = 3n^2 n^2 = 842/3 n = sqrt(842/3) = 16.753 Since we can only have whole number answers, our answer must be either 16 or 17 A(16) = 600.625 A(17) = 600.5294 So our answer will be 17 floors
