QUESTION 1

Find all the local maxima, local minima, and saddle points of the given function. f(x,y) = 2x2 + 3xy + 4y2 - 5x + 2y Select the correct choice below and ll in any answer boxes within your choice. '3' A- There are local maxima located at (Simplify your answers. Type ordered pairs. Use a comma to separate answers as needed.) Cir B. There are no local maxima. Select the correct choice below and ll in any answer boxes within your choice. '3' A- There are local minima located at (Simplify your answers. Type ordered pairs. Use a comma to separate answers as needed.) Cir B. There are no local minima. Select the correct choice below and ll in any answer boxes within your choice. '3' A- There are saddle points located at (Simplify your answers. Type ordered pairs. Use a comma to separate answers as needed.) (:2: B. There are no saddle points. Find the total area of the shaded regions. The total area of the shaded regions is (Type an integer or decimal rounded to three \_2 decimal places as needed.) A company sells square carpets for $5 per square foot. It has a simplied manufacturing process for which all the carpets each week must be the same size, and the length must be a multiple of a half foot. It has found that it can sell 100 carpets in a week when the carpets are 3 ft by 3 ft, the minimum size. Beyond this, for each additional foot of length and width, the number sold goes down by 4. What size carpets should the company sell to maximize its revenue? What is the maximum weekly revenue? Write the equation for the revenue, R, the company will earn as function of the length, x, of the carpet squares sold. R(x) = D The carpet size that maximizes revenue has a length of V The maximum weekly revenue is $ (Type integers or decimals rounded to two decimal places as needed.)