Your financial company has two kinds of investment products: P1 and P2. These are sold to the public in units where one unit of P1 costs $600 and one unit of P2 costs $400. One can by any non-negative amount of units of P1 or P2.

Each unit of P1 contains 20 shares of Company A, 12 shares of Company B, and 40 shares of Company C. Each unit of P2 contains 30 shares of Company A, 48 shares of Company B, and 20 shares of Company C.

A particular investor states that she requires at least 600 shares of Company A, at least 240 shares of Company B, and at least 800 shares of Company C. How may units of P1 and P2 should the investor purchase so that her requirements above are satisfied and the total cost of her investment products is minimized? What is the least total cost? Provide a complete solution to this linear programming problem. You may assume there actually is a least total cost for the given requirements; you need not verify this.