In order to package one of their products, Acme Box Co. needs to construct a box whose bottom side has length 3 times its width. The material used to build the top and bottom of the box cost $10 per square foot, while the material used to build the four sides of the box cost $6 per square foot. The box must have a volume of 50 cubic feet. (a) In terms of the length ` of the bottom, the width w of the bottom and the height h of the box (all measured in feet), write a formula for the cost C (in dollars) to construct a box of length `, width w and height h. (b) Given the other conditions specified in the problem, express C as a function of a single variable. (c) Determine the dimensions of the box that minimize the cost. Be sure to justify that you have found dimensions that produce the minimum cost. (You’ll be fired if you submit the maximum cost to your boss!) To the nearest dollar, how much will it cost to build the box at these dimensions?