In a basketball and soccer ball factory, the Marketing Manager has to decide the best way to spend the resources allocated to advertising. Each of the sponsored soccer teams requires 120 soccer balls. Each basketball team requires 32 basketballs. Soccer coaches receive $300,000 in ball sponsorships, and basketball coaches receive $1,000,000. The budget for promotions amounts to $30,000,000. The factory has a limited supply (4 liters, that is, 4,000 cubic centimeters) of polyester, a compound that is used in the manufacture of promotional balls. Each basketball requires 3cc (cubic centimeter) of polyester and each soccer ball requires 1cc (cubic centimeter). The manager wishes to sponsor as many basketball and soccer teams as his resources allow. a) Formulate a set of linear equations to describe the objective function and constraints. Solve using the simplex method.