Problem: The AB Company makes two different products, namely, A and B. They have been selling product A for $59 and product B for $89. The production costs are $30 for A and $50 for B, plus an additional $20,000 in fixed costs. The market for these products is extremely competitive. Not only will these products compete with other brands, but they will compete with each other. In order to sell all the As that they produce, they will have to reduce the price (currently $59) by $0.01 for each A sold and by $0.005 for each B sold. Similarly, the price of B (currently $89) must be reduced by $0.005 for each A sold and by $0.02 for each B sold. How many units of each product should be made, and what their prices should be, in order to maximize profits?