1. Solve this system and find the product of its solutions. x + y = 7 2x – y =8 2. The feasible region for a set of constraints has vertices (2,0), (8,2) and (4,-6). Find the max and min vales for the objective function; S= 2y + x 3. Graph the feasible region for the following constraints and find its vertices. y≤ 1/4x + 5 y≤ -x + 6 y≥ 0 x≥ 0

Lesson 3.5 Linear Programming

 Graph the feasible region for each set of constraints. Then, identify the vertices of the feasible region and find the maximum and minimum values if any for the given objective function. S = 3x - y Constraints: y ≤ -x + 4 y ≤ x + 2 x ≥ 0 y≥ 0

The feasible region for a set of constraints has vertices at (-4,0), (3,3), (6,2) and (4,1). Given this feasible region, find the maximum and minimum values of each objective function. #2 P = 4x – 6y

 A farmer has 10 acres to plant wheat and rye. Each acre of wheat costs $200 to plant and each acre of rye costs $100. He has a total of $1200 to spend in planting. Each acre of wheat will make a $500 profit and each acre of rye will make a profit of $300. How many acres of each should be planted to maximize profit? Corner point Value of Objective Function

 A gold processor has two sources of gold ore. Gold from source A costs $20 per ton to process and gold from source B costs $10 to process. Costs must be kept to less than $80 per day. Each source has limited hours of processing each day. Source A can operate for 6 hours per day and source B can operate for 12 hours. The total hours must be kept under 60 hours. If gold from source A yields 2 oz of gold per ton and gold from source B yields 3 oz per ton, how many tons of ore must be produced each day to maximize the profits? Corner point Value of Objective Function

 Bob builds small and large tool sheds. He only has enough supplies to manufacture 30 total sheds. Each small shed requires 6 hours of time to manufacture and each large shed requires 30 hours. He has no more than 300 hours to work on the sheds. If the small shed makes a profit of $130 and the large shed makes a profit of $250, how many of each type of shed should be build to maximize his profit? Corner point Value of Objective Function

Lesson 3.5 Worksheet 3.5.2