Problem #3-Minimizing Cost; Another Box: The base of a rectangular box is to be twice as long as it is wide. The volume of the box must be 256 cubic-inches. The material for the top of the box costs $0.10 per square-inch, and the material for the sides and bottom costs S0.05 per square-inch. Your objective is to build the least costly box that fulfills these requirements Step 1: Build the objective function. Let x denote the width of the bottom of the box. Build the function C(x) that calculates the total cost to build the box, as a function of the width of the bottom of the box. Draw a diagram if it helps. Step 2: Find the critical values. Using the derivative, find the critical values of the objective function Step 3: Classify critical values. Perform an appropriate test to classify the critical value(s) from Step 2 Step 4: Answer the question. What are the dimensions of the box that fits the requirements and is cheapest to produce? What is the cost of the cheapest box that fits the requirements?