Consider a product mix problem, where the decision involves determining the optimal production levels for products X and Y. A unit of X requires 4 hours of labor in department 1 and 6 hours of labor in department 2. A unit of Y requires 3 hours of labor in department 1 and 8 hours of labor in department 2. Currently, 1000 hours of labor time are available in department 1, and 1200 hours of labor time are available in department 2. Furthermore, 400 additional hours of cross-trained workers are available to assign to either department (or split between both). Each unit of X sold returns a $50 profit, while each unit of Y sold returns a $60 profit. All units produced can be sold. Formulate this problem as a linear program, and use Excel Solver or QM for Windows to obtain a solution for the maximum profit and the decision variables. Round your answers to whole numbers. (Hint: Consider introducing other decision variables in addition to the production amounts for X and Y.)