Solve each optimization problem.

a) Let x and y be two positive numbers such that x+2y=50 and (x+1)(y+2) is a maximum.

b) We are going to fence in a rectangular field. If we look at the field from above, the cost of the vertical sides are $10/ft, the cost of the bottom is $2/ft, and the cost of the top is $7/ft. If we have $700, determine the dimensions of the field that will maximize the enclosed area. Your solution should include a sketch of the problem.