The Ininob Manufacturing Company produces three products; widgets, yamis, and zots. The company is trying to determine its production schedule for these products for the next month. The company sells widgets for P500 each, and zots for P400 each. At these prices, up to 200 widgets and 30 zots can be sold. The price for yq.mis has not been decided. Two prices are under consideration -P500 and P600. At the P500 price, up to 100 can be sold. At the P600 price, up to 60 can be sold. Ininob purchases the raw material from which all three products are produced from a single firm. Widgets require 0.1 tons of raw materials for each one produced. Yamis requires 0.2 tons each: and zots require 0.3 tons each. Because of a shortage, there are only 50 tons of raw materials available for production of all thre products. The cost of the raw material is P200 per ton. The first step in the production process for all three products is a molding and heating operation. This requires a special purpose machine. A maximum of 400 hours is available on this machine. No additional hours can be obtained since the machine is already operating three shifts. The variable cost of operating this machine is P80 per hour. Each widget requires 1 hour on the machine; each yami, requires 2 hours; and each zot requires 0.5 hours. After the molding and heating operations described above, the product is finished. Zots are finished on a zotting machine. It costs P5000 to set up this machine and P100 per zot finished. Widgets and yamis are finished on a widgeting machine. There is a cost of P10000 to set up this machine. However, once the machine is set up, the machine can finished, either widgets or yamis or both. The variable cost of operating this machine is P100 per unit for either yamis, or widget. Formulate the problem as an integer linear programming problem.