Quiz 5 - Mini Practice Review

*Please show all work and steps so I can compare my work and make sure I am understanding these concepts.

Minimize the function M = 2x + 2y subject to 2x+ y = 32 and find the values of x and y at which M is minimized. The minimum value of M is and it occurs when x is and y isA box (with no top) will be made by cutting squares of equal size out of the comers of a 37 inch by 53 inch rectangular piece of cardboard, then folding the side aps up. Find the maximum volume of such a box. ROUND TO THE NEAREST CUBIC INCH. The maximum volume is D cubic inches. The height of a cylinder is increasing at a rate of 7 inches per second, while the radius is decreasing at a rate of 3 inches per second. If the height is currently 60 inches, and the radius is 12 inches, then nd the rate of change in the volume. ROUND YOUR ANSWER TO ONE DECIMAL PLACE. (The formula for the volume of a cylinder is V = atr2h. ) . 3 In The rate of change in the volume is D sec