I need all work shown for all the problems.

solve the problem analytically. 1) Of all numbers whose sum is 360, find the two that have the maxis where soy - 360. um product That is maximize Q = Xy, A) 10 and 350 B) 160 and 1.80 C) 179 and 161 D) 1 and 35, Solve the problem. 7) A carpenter is building a rectangular room with a fixed perimeter of 450 it. What are the din sinns of the Largest room that can be built? What is its area? A) 120 ft x 360 fit, 43.200 62 B) 240 ft x 240 1: 57,500 12 C) 1210) At = 120 6: 1:1400 82 D) 49 P x 432120,736 67 3) A piece of molding 151 om long is to be cut to form a nectar ar picture frame. What d enclose the largest area? Round to the nearest hundredth, if necessary. A) 12 29 can . 37.75 am C) 30.2 cm x 30.2 cm D) 1279 am. 1279a {)A company wishes to manufacture a box with a volume of 40 cubic feet that is open on top and is brice as long as it is wide. Find the width of the box that can be produced using the mining punt of material Round to the nearest tenth, if necessa A) 64ft B) 3.6 ft 932At D) 72 8 5) A company is constructing an open-top, square-based, rectangular metal tank that will have a volume of 5 47 At3. What dimensions yield the minimum surface area? Round to the nearest tenth, if necessary. A) 45 At x 45 f . 230 6) 97 A . 971 x 05At () 3.6 ft =