The manufacturer makes 2 models of elliptical cross-training exercise machines. Times for assembling, finishing and packaging model X are 3 hours, 3 hours, and 0.8 hour, respectively. Times for model Y are 4 hours, 2.5 hours, and 0.4 hour. Total times available for assembling, completing and packaging are 6000 hours, 4200 hours, and 950 hours, respectively. Profits per unit are $300 for model X and $375 for model Y. Find optimal production level for every model? Find the optimal profit. Illustrate all work.