1|.I"'.|'hat point on the line 3; = 3x + 2 is closest to the origin? r:) Let D be the distance between the two points. What is the objective function in terms of the xcoordinate? n=o [Type an expression} a. Find the radius and height of a cylindrical soda can with a volume of 322 cm" that minimize the surface area. b. Compare your answer in part (a) to a real soda can, which has a volume of 322 cm", a radius of 3.1 cm, and a height of 10.9 cm, to conclude that real soda cans do not seem to have an optimal design. Then use the fact that real soda cans have a double thickness in their top and bottom surfaces to find the radius and height that minimizes the surface area of a real can (the surface areas of the top and bottom are now twice their values in part (a)). Are these dimensions closer to the dimensions of a real soda can? a. Write a function for the surface area of the soda can, S, in terms of the radius, r. S = (Type an expression.)A boat on the ocean is 3 mi from the nearest point on a straight shoreline; that point is 11 mi from a restaurant on the shore. A woman plans to row the boat straight to a point on the shore and then walk along the shore to the restaurant. Complete parts (a) and (b) below. 3 mi 11mi a. If she walks at 3 mi/hr and rows at 2 mi/hr, at which point on the shore should she land to minimize the total travel time? Let x be the distance between the nearest point on shore and the point she lands on shore. If T is the time it takes her to get to the restaurant, what is the objective function? T= (Type an expression.)Suppose an airline policy states that all baggage must be box-shaped with a sum of length, width, and height not exceeding 114 in. What are the dimensions and volume of a square-based box with the greatest volume under these conditions? Write a function for the volume V of the box in terms of w, one of the edges of the square bottom. V= (Type an expression.)