1. Monday WARM-UP: TrueFalseStatementCorrected Statement F 1. Constraints are conditions written as a system of equations Constraints are conditions written as a system of inequalities T 2. The feasible region is where all the constraints are satisfied. T 3. The objective function represents the quantity that is to be minimized or maximized F 4. The optimal solution is always the largest value of the objective function The optimal solution is always a maximum (like profit) or a minimum (like cost)

2. 1.Find decision variables 2.Find the objective function 3.Find the constraints A.List the items related to the decision variables B.Use math symbols to combine the decision variables to the limits of each item 4.Graph the constraints (linear inequalities) 5.Find corner points A.A corner point is found where two inequalities intersect. Use substitution or cancelation to solve these two inequalities to find the exact coordinate (x, y). 6.Substitute the corner points into the objective function to find the solution (either the min. or max.) v

3. Using the graph below, determine the corner points, optimal solutions, and two constraints.

4. Wednesday WARM-UP: A farmer has a field of 70 acres in which he plants potatoes and corn. The seed for potatoes costs $100/acre, the seed for corn costs $10/acre and the farmer has set aside $3000 to spend on seed. The profit per acre of potatoes is $150 and the profit for corn is $80 an acre. Find the optimal solution for the farmer. Write the constraints for the problem. Write the Objective Function. Graph the constraints and find the corner points. To find the optimal solution you are looking for the maximum. Use your corner points to find the maximum profit.