(1 point) According to U.S. postal regulations, the girth plus the length of a parcel sent by mail may not exceed 108 inches, where by "girth" we mean the perimeter of the smallest end. What is the largest possible volume of a rectangular parcel with a square and that can be sent by mail? Such a package is shown below. Assume y > 3:. What are the dimensions of the package of largest volume? .V x Find a formula for the volume of the parcel in terms of x and y. Volume = The problem statement tells us that the parcel's girth plus length may not exceed 108 inches. In order to maximize volume, we assume that we will actually need the girth plus length to equal 108 inches. What equation does this produce involving x and y? Equation: ::: Solve this equation for y in terms of x. y : :2: Find a formula for the volume V(x) in ten'ns of x. V(x) = iii What is the domain of the function V? Note that both x and y must be positive; consider how the constraint that girth plus length is 108 inches limits the possible values for x. Give your answer using interval notation. Domain: u: Find the absolute maximum of the volume of the parcel on the domain you established above and hence also determine the dimensions of the box of greatest volume. Maximum Volume = 555 Optimal dimensions: at = 2!! and y = (1 point) A rancher wants to fence in an area of 2500000 square feet in a rectangular field and then divide it in half with a fence down the middle, parallel to one side, as shown below. What is the shortest length of fence that the rancher can use? Length of fence = 555 feet. (Round to three decimal places as needed.) (1 point) Find the dimensions of the rectangle with area 324 square inches that has minimum perimeter, and then find the minimum perimeter. 1 . Dimensions: 2. Minimum perimeter: Enter your result for the dimensions as a comma separated list of two numbers. Do not include the units. (1 point) A cattle rancher wants to enclose a rectangular area and then divide it into five pens with fencing parallel to one side of the rectangle (see the figure below). There are 470 feet of fencing available to complete the job. What is the largest possible total area of the five pens? Largest area = 5!! Gnclude mite) (1 point) A cattle rancher wants to enclose a rectangular area and then divide it into six pens with fencing parallel to one side of the rectangle (see the figure below). There are 400 feet of fencing available to complete the job. What is the largest possible total area of the six pens? Largest area = Gnclude Halts)