I need help with these two problems please, and please answer all parts of the questions and make it it legible. You can see from the pics how many parts of the problems their are.

Find the dimensions of the closed rectangular box with maximum volume that can be inscribed in the unit sphere. The dimensions are E. (Type exact answers, using radicals as needed. Use a comma to separate answers as needed.) Part 1 of 7 Points: 0.6 of 2 During the 1920s, Charles Cobb and Paul Douglas modeled total production output P (of a firm, industry, or entire economy) as a function of labor hours involved x and capital invested y (which includes the monetary worth of all buildings and equipment). The Cobb-Douglas production function is given by P(x,y) = kx y , where k and a are constants representative of a particular firm or economy. Complete parts a. and b. below. . . . . . a. Show that a doubling of both labor and capital results in a doubling of production P. Which of the following does it make the most sense to evaluate to show this? O A. P(x,2y) O B. P(2x,2y) O C. 2P(x,y) O D. P(2x,y)