This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise Find two numbers whose difference is 78 and whose product is a minimum. Step 1 If two numbers have a difference of 78 and we let x represent the smaller of these two numbers, then the larger of these two numbers is given by the following. 78 + x r + 78 Stop 2 We will now write a function that is the product of our two numbers, where x represents the smaller number and x + 78 represents the larger number as follows. (( x ) = xx +[ = X +0Consider the following problem: a box with an open top is to be constructed from a square piece of cardboard, 3 feet wide, by cutting out a square from each of the four corners and bending up the sides. Find the largest volume that such a box can have. (a) Draw several diagrams to illustrate the situation, some short boxes with large bases and some tall boxes with small bases. Find the volume of each configuration. Does it appear that there is a maximum volume? If so, estimate it. (b) Draw a diagram illustrating the general situation. Let x denote the length of the side of the square being cut out. Let y denote the length of the base. (c) Write an expression for the volume V in terms of both x and y. V = x( 36 - 2x )- (d) Use the given information to write an equation that relates the variables x and y. (e) Use part (d) to write the volume as a function of only x. V(x) =