1. Astorage shed is to be built in the shape of a box with a square base. It is to have a volume 01'891 cubic feet. The concrete for the base costs $5 per square foot, the material for the roof costs $6 per square foot, and the material for the sides costs $4.50 per square toot. Find the dimensions of the most economical shed. Let x represent the length of one of the sides of the base and let C represent the cost of the shed. What is the objective function? c = (Type an expression.) The interval of interest of the objective function is . (Simplify your answer. Type your answer in interval notation.) The length of one side of the shed's base is ft. The height of the shed is ft. Consider the following descriptions of the vertical motion of an object subject only to the acceleration due to gravity. (Note: the acceleration due to gravity is 9.8 m/s .) a. Find the velocity of the object for all relevant times. b. Find the position of the object for all relevant times. c. Find the time when the object reaches its highest point (What is the height?) d. Find the time when the object strikes the ground. A payload is released at an elevation of 500 m from a hot-air balloon that is rising at a rate of 12 m/s. . . . a. v(t) = b. s(t) = c. The object's highest point is m at time t = s. (Simplify your answers. Round to two decimal places as needed.) d. t= (Simplify wnuIr anewor Round to twin decimal places ac noorlord )3. Find the area of the region bounded by the graph of f()() = x(x + 3)(x + '1) and the x-axie 0n the interval [- 3,0]. The area is . (Simplify your answer.)