10.8 Linear Programming.

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Presentation transcript:

10.8 Linear Programming

Linear Programming Ex1) Use the system of constraints below to maximize the objective function z = -0.4x + 3.2y. Corner Points

Linear Programming Ex1) Use the system of constraints below to maximize the objective function z = -0.4x + 3.2y. (x,y) z = -0.4x + 3.2y (0,2) (0,5) (1,6) (4,0) (5,0) (5,2)

Linear Programming Ex2) Use the system of constraints below to minimize the objective function z = 2x + 3y. Corner Points

Linear Programming Ex2) Use the system of constraints below to minimize the objective function z = 2x + 3y. (x,y) z = 2x + 3y (0,2) (0,5) (2,0) (6,0) (6,5)

Linear Programming Ex3) A calculator company makes scientific and graphing calculators. There is a demand for at least 100 scientific and 80 graphing calculators a day; however, due to materials, no more than 200 scientific and 170 graphing calculators can be made daily. To satisfy a shipping contract, at least 200 calculators must be shipped each day. If each scientific calculators results in a loss of $2, but each graphing calculator gains a profit of $5, how many of each type should be made to maximize profit? a) Identify the system of constraints and the objective function. x = sci calcs y = graph calcs

Linear Programming b) Graph the system of constraints to find the corner points Corner Points

Linear Programming c) Plug in the corner points to determine what amount of each type of calculator would maximize profit. (x,y) P = -2x + 5y (100,100) (100,170) (120,80) (200,80) (200,170)

Linear Programming Ex4) A toy manufacturer makes bikes and wagons. It requires 2 hours of machine time and 4 hours of painting time to produce a bike. It requires 3 hours of machine time and 2 hours of painting time to produce a wagon. There are 12 hours of machine time and 16 hours of painting time available per day. The profit on bikes is $12 and the profit on wagons is $10. How many bikes and wagons should be produced per day to maximize profit? What is the maximum profit per day?

10.8a Linear Programming Homework: Page 821 # 9, 11 Worksheet #1 - 4