1. Solve the systems of inequalities graphically, state if the feasible region is bounded or unbounded, and determine the corner points. 1.1 3x - y 6 3x + y 9 x, y 0

1.2 3x - 6y 12 x + y 7 x, y 0

2. A tent company produces two types of tents: standard and expedition. The standard type requires 3 hours of cutting and 7 hours of assembly. The expedition type requires 5 hours of cutting and 5 hours of assembly. The company has at most 60 hours a month for cutting and at most 100 hours a month for assembly. How many tents should be produced to maximize the profit if the company makes a profit of $80 on each standard tent and a profit of $100 on each expedition tent?

3. Solve the linear programming problems by drawing the feasible solution region and using the corner point table. 3.1 Maximize: z = 4x + 5y subject to: x + y 4 x - y -2 x 3 x 0, y 0

3.2 Minimize: z = 12x + 13y Subject to: 1.5x - 3y 6 2x + 2y 14 x, y 0

4. A dietician needs to plan a diet for a patient using two different food combinations to meet the patient's needs. Each container of Food A contains 1 units of Additive #1 and 3 units of Additive #2. Each container of Food B contains 1 units of Additive #1 and 6 units of Additive #2. The patient needs at least 5 units of Additive #1 and at least 18 units of Additive #2. How many containers of each food should the dietician use to meet the patients needs and minimize the cost if one container of Food A costs $5 and each container of Food B costs $9?

5. A fast-food chain plans to expand by opening several new restaurants. The chain operates two types of restaurants: drive-through and full-service. A drive-through restaurant costs $100,000 to construct, requires 5 employees, and has an expected annual revenue of $200,000. A full-service restaurant costs $150,000 to construct, requires 15 employees, and has an expected annual revenue of $500,000. The chain has $2,400,000 in capital available for expansion. Labor contracts require that they hire no more than 210 employees, and licensing restrictions require that they open no more than 20 new restaurants. How many restaurants of each type should the chain open in order to maximize the expected revenue? What is the maximum expected revenue? How much of their capital will they use and how many employees will they hire?