3. The monthly profit (in dollars) of Bond and Barker Department Store depends on the level of inventory x (in thousands of dollars) and the floor space y (in thousands of square feet) available for display of the merchandise, as given by the equation ( ) 2 2 , 0.02 15 39 25 20, 000P x y x y xy x y= ? ? + + + ? Computer /P x ? ? and /P y ? ? when x = 4000 and y = 150. Interpret the results. Repeat with x = 5000 and y = 150 4. The productivity of a country is given by ( ) 0.438 0.562, 15.14f x y x y=, where x is the amount of labor and y is the amount of capital. a. Does this represent a Cobb-Douglas Function? Why or why not? b. Determine the partial derivatives xf and yf , then evaluate when x = 69 and y = 53. c. Interpret the results. Is it better to increase labor or capital by one unit? 5. Find the relative maximum and minimum values and saddle points using the D-Test for ( ) 2 2 2, 242f x y y x x y= + ? . Show all partial derivatives and work! 6. A company produces two types of solar panels per year: x thousand of type a and y thousand of type B. The revenue and cost equations, in millions of dollars, for the year are given as ( ), 3 2R x y x y= + and( ) 2 2 , 3 8 7 73 3C x y x xy y x y= ? + + ? ? . Determine how many of each type of solar panel should be produced per year to maximize profit. What is the maximum profit? Use the D-Test and show all partial derivatives and work.

3. The monthly profit (in dollars) of Bond and Barker Department Store depends on the level of inventory x (in thousands of dollars) and the floor space y (in thousands of square feet) available for display of the merchandise, as given by the equation P(x,y) = O.02x2 15y2 + xy+ 39x+ 25y 20,000 Computer 6P / 6x and 6P / By when x = 4000 and y = 150. Interpret the results. Repeat with x = 5000 and y = 150 4. The productivity of a country is given by f (x, y) = 15 .14360'438y0'562 , where x is the amount of labor and y is the amount of capital. a. Does this represent a Cobb-Douglas Function? Why or why not? b. Determine the partial derivatives fl and fy , then evaluate when x = 69 and y = 53. c. Interpret the results. Is it better to increase labor or capital by one unit? 5. Find the relative maximum and minimum values and saddle points using the D-Test for f(x, y) = 242y2 + x2 xzy. Show all partial derivatives and work! 6. A company produces two types of solar panels per year: x thousand of type A and y thousand of type B. The revenue and cost equations, in millions of dollars, for the year are given as R (x, y) = 3x+ 2 y and C( x, y) = x2 3xy + 8y2 + 7x 73y 3 . Determine how many of each type of solar panel should be produced per year to maximize prot. What is the maximum profit? Use the D-Test and show all partial derivatives and work