Maximizing Profit from Gadget Production

A factory produces two types of gadgets: gadget X and gadget Y. The production costs are different: producing one gadget X costs $5.00 while one gadget Y costs $7.50. The factory has a budget of $4,500 for production this month. Due to a promotional offer, the factory gains an additional $600 for every 100 gadgets of either type sold. If the factory wants to maximize its profits, how many gadgets of each type should they produce and sell, assuming they can produce at most 700 gadgets total?

Let:

• x = number of gadget X produced
• y = number of gadget Y produced

The profit P can be expressed as:

$$ P = 600 imes (x + y) - (5x + 7.5y) $$

What is the maximum profit represented as a decimal in thousands (for example, if the answer is 12,000, write 12)?