Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

enter image description here

I recognize that this is an optimization problem and I need to take the derivative set it equal to 0 and plug it back into the original function but I am having trouble figuring out the original function.

share|improve this question

1 Answer 1

Let the height, width and length of the box be $h,w,l$ respectively. Since the top and bottom are squares, let $l = w = a$. Therefore, the volume of the box is $ha^2 = 14.71$ and the total material cost is $f(a,h) = 2a^2 + 4ah$ which is the area of the top and bottom ($2a^2$) and the 4 sides ($4ah$).

Hint: You can reduce $f$ to a function of a single variable ($g(a)$ or $g(h)$) using $ha^2 = 14.71$ and then find its derivative $g'$.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.