Patsy, Inc., manufactures two products, X and Y. Each product must be processed in each of three departments: machining, assembling, and finishing. The hours needed to produce one unit of product per department and the maximum possible hours per department follow: Production Hours per Unit Department X Y Maximum Capacity in Hours Machining 2 1 420 Assembling 2 2 500 Finishing 2 3 600 Other restrictions follow: X 50 Y 50 The objective function is to maximize profits where profit=$4X+$2Y. Given the objective and constraints, what is the most profitable number of units of X and Y, respectively, to manufacture? (a) 150 and 100 (b) 165 and 90 (c) 170 and 80 (d) 200 and 50