The Gillette Company produces two popular battery-operated razors, the M3Power™ and the Fusion Power™. Because of demand, the number of M3Power™ razors is never more than one-half the number of Fusion Power™ razors. The factory's production cannot exceed 800 razors per day. Let x = the number of M3Power™ razors and y = the number of Fusion Power™ razors produced per day.
a) Write a system of inequalities to express the conditions of the problem.
b) Graph the feasible region of the system on a coordinate plane.
c) Determine the maximum profit if each M3Power™ razor sells for 20 and each Fusion Power™ razor sells for 30.