1. (1/24 and 1/27) Bellwork: 1)List 2 things we’ve discussed this semester 2)What is one positive thing you’d be willing to share?

2. Overview- Linear Programming: Goal: Find the minimum and or Maximum Pieces: Objective Function- often profit or cost, the thing you want to minimize or maximize. What we use to check possible solutions. Constraints- inequalities representing the limits or restrictions of the situation

3. You need to buy some filing cabinets. The Alpha cabinet costs $10 per unit, requires six square feet of floor space, and holds 8 cubic feet of files. The Beta cabinet costs $20 per unit, requires 8 square feet of floor space, and holds 12 cubic feet of files. You have been given $140 for this purchase. The office has room for no more than 72 square feet of cabinets. How many of which model should you buy, in order to maximize storage volume? Step 1) Break down the problem and list your variables, objective function, and constraints

4. You need to buy some filing cabinets. The Alpha cabinet costs $10 per unit, requires six square feet of floor space, and holds 8 cubic feet of files. The Beta cabinet costs $20 per unit, requires 8 square feet of floor space, and holds 12 cubic feet of files. You have been given $140 for this purchase. The office has room for no more than 72 square feet of cabinets. How many of which model should you buy, in order to maximize storage volume? Step 1) Break down the problem and list your variables, objective function, and constraints

5. Step 2) Graph all constraints marking area where all are shaded (this is called the feasible region)

6. Step 3)Label all intersections surrounding the feasible region. These are your possible solutions.

7. Step 4)Test each possible solution you found by plugging them in to the objective function. (Make sure they make sense!)

8. What were we being asked? The Final answer is (8, 3), so we should order 8 alpha cabinets and 3 beta cabinets