Suppose an airline policy states that all baggage must be box-shaped with a sum of length, width, and height not exceeding 156 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.) A storage shed is to be built in the shape of a box with a square base. It is to have a volume of 539 cubic feet. The concrete for the base costs $6 per square foot, the material for the roof costs $5 per square foot, and the material for the sides costs $3.50 per square foot. 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.) Find the point P on the line y= 5x that is closest to the point (52,0). What is the least distance between P and (52,0)? E> Let D be the distance between the two points. What is the objective function in terms of one number, x? D=D (Type an expression.) A rectangular flower garden with an area of 494 m" is surrounded by a grass border 1 m wide on two sides and a 2 m wide on the other two sides as shown in the figure. What dimensions of the garden minimize the combined area of the garden and borders? 2 m Flower garden 1 m Let h be the vertical height of the garden and let A be the total area of the garden and borders. Write the objective function. A = (Type an expression.)An island is 3 mi from the nearest point on a straight shoreline; that point is 12 mi from a power station (see gure). A Utility company plans to lay electrical cable underwater from the island to the shore and then underground along the shore to the power station. Assume that is costs $2800/mi to lay cable underwater and $1400lmi to lay underground cable. At what point should the underwater cable meet the shore to minimize the cost of the project? Island 1 \\ ~\\ Power 9 'A \\ Station Write an equation for the total cost, C, as a function of x, where x is the distance from the shoreline closest to the island and the point where the cable leaves the shore. C = (Type an expression.)