Example: The development of a new retail product calls for a cardboard box to store the item. The company selling the new product would like the box to have a square base and a volume of 686 cubic inches. The cardboard to construct the top and bottom of the box cost 10 cents per square inch while the cardboa rd to construct the sides of the box cost 5 cents per square inch. We will take the following steps to nd the minimum cost box! (a) Draw a picture to model the situation {you don't need to include it here}. Label the dimensions of the square base with x and the height of the box with h. Recall the volume of such a box is given by xzh. Use this information to write down the volume constraint! (bi Use the volume constraint to express h in terms of x! [c] Express the cost of the box in terms of x and h. Hint: When you decompose the box you will get 2 squares and 4 rectangles! Make sure to include the cost for each! (d) Use your answer from [hi to express the cost function (from [cl] as a function of at only! Hint : substitute for ill to} Use calculus to nd the xvalue that leads to minimum cost. After that, give the dimensions and cost of the minimum cost box