Shek 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 and the maximum possible hours per department are provided below. The below function is to maximize profits if profit equal P4X + P2Y . Given the objective function and constraints, what is the most profitable number of units of X and Y, respectively , to manufacture?

Maximum Capacity

Production Hours per Unit In hours

Department X Y

Machining 2 1 420

Assembling 2 2 500

Finishing 2 3 600

Other instruction follows:

X = 50

Y = 50