Imagine your company has 3 products: TVs, Stereos and Speakers. The profit is $100 per TV, $30 per Stereo and $30 per Speaker. Each of these products uses the same 5 parts (but in different amounts): Chassis, Picture Tube, Speaker Cone, Power Supply and Electronics. You have a total of 450 Chassis, 250 Picture Tubes, 900 Speaker Cones, 450 Power Supplies, and 600 Electronic parts. One TV uses 1 Chassis, 1 Picture Tube, 2 Speaker Cones, 1 Power Supply and 2 Electronic Parts. One Stereo uses 1 Chassis, 0 Picture Tube, 2 Speaker Cones, 1 Power Supply and 1 Electronic Part. One Speaker uses 1 Chassis, 0 Picture Tubes, 1 Speaker Cone, 0 Power Supply and 1 Electronic Part. Based on this information, please calculate the optimal product mix that would maximize profitability, while not exceeding inventory constraints.