A microprocessor chip is being designed with a given rectangular area A. Show that the chip with the minimum perimeter should be a square. Let the length and width of the chip be x and y, respectively. An equation involving the three variables A, x, and y is (Type an equation.) If P is the perimeter of the rectangle, then an equation involving the three variables P, x, and y is (Type an equation.) Use the equation involving A to rewrite the equation involving P so that it uses only P and x. The result describes P as a function of the single variable x. (Type an equation.) Find - dP dx dP dx Set the derivative equal to zero, and solve the resulting equation to find the value for x for which a minimum may occur. What is the result? Note that because x is the length of the chip, it must be positive. x = To check that this x-value does indeed make P a minimum, use the second derivative. Find d-p dx 2 d-p dap At the x-value found earlier, is This means P a minimum at that x-value. dy 2Find the y-value that corresponds to the x-value found earlier. y= Why does it follow that the chip with the minimum perimeter should be a square? O A. Since y = x, the sides of the rectangle have the same length. O B. Substituting x and y into the formula for the perimeter yields P =0. Since the perimeter cannot be negative, this must be the minimum perimeter. O C. Since x= 2y, the length of the chip is exactly twice its width. O D. Substituting x and y into the formula for the area confirms that the area of the chip is A