1. A company produces three different products (A,B,C). According to the previous order experiences, everybody, who buys product A, also buys product B. Because of this situation, the company wants to produce A and B with the same quantity. All of the products are produced by using gold and product A needs 5 grams of gold, product B needs 8 grams of gold, product C needs 7 grams of gold. However, the company has only 0.5 kilogram of gold and storage space limit for the products. Total storage space of the company is 100 units and it is known that it can be completely filled. Produced one unit of product A uses 4 units of storage space, one unit of product B uses 1 units of storage space, one unit of product C uses 3 units of storage space. The costs for the production of each product is 5$2$ and 6 \$ respectively (A, B, C). Formulate a Linear Programming Model for the company to find the optimum production quantities of the products. (30P)