A canvas wind shelter for the beach has a back, two square sides, and a top (see the figure to the right). If 216 square feet of canvas is to be used, find the dimensions of the shelter for which the space inside the shelter (the volume) is maximized. The problem asks to maximize the volume of the shelter. Let V be the volume of the shelter. Next assign letters to other quantities that may vary. Let s represent the length of one of the square sides of the wind shelter and let z be the width of the wind shelter. Write the equation for the volume using the variable s and z. Note that the ends of the figure are squares V=(Simplify your answer.) Recall that 216 square feet of canvas is to be used. Which of the following formulas represents the total surface area of the canvas? O A. 216 =25 + 2sz O B. 216 = 252 + SZ O C. 216=$2 + 25z OD. 216 =$2 + SZ Use the constraint equation (the equation for the surface area) to simplify the objective equation (volume) in such a way that it becomes a function of only one variable. Begin by solving the constraint equation in terms of z. 2 = Take the value of z and use it to find the volume in terms of one variable. Find V(s). V(s) = (Simplify your answer. Do not factor.) What is the next step O A. Use the constraint equation to find the critical values. O B. Substitute V(s) into the constraint equation. O C. Find the critical values with V"(s) O D. Find the critical values with V'(s). Find V'(s), which will be used to find the critical points for the objective equation. V'(s) = (Simplify your answer.)Find V'(s), which will be used to find the critical points for the objective equation. V'(s) = (Simplify your answer.) Find the critical points of V(s), when V'(s) = 0. Reject any negative solutions because it is not feasible given the context of the question. V'(s) = 0 s = ](Simplify your answer.) What is the next step? O A. Test whether the critical value is a maximum or minimum using V"(s). O B. Use the values of s to find the surface area. O C. Test whether the critical value is a maximum or minimum using V(s). O D. Find the value of z using the objective function. Use the previously found value of V'(s) to find V"(s) to determine if the critical point is located at a relative minimum or maximum. V"(s) = (Simplify your answer. Do not factor) Let a be the previously found critical value. Test using the critical value a. V"(a) = (Simplify your answer.) To find the value of z, substitute the critical value a into the constraint equation and simplify. z = (Simplify your answer.)