1. Do This Problem Right Now  Given Find the minimum and maximum for equation, (0, 8) (4, 0) (0, 2) (2, 0) verticesC = 2x + 3yMin/Max (0, 8) C = 2(0) + 3(8) 24 (0, 2) C = 2(0) + 3(2) 6 (2, 0) C = 2(2) + 3(0) 4 (4, 0) C = 2(4) + 3(0) 8 10/16/2015 11:07 AM10/16/2015 11:07 AM10/16/2015 11:07 AM1

2. LINEAR PROGRAMMING Day 2 Section 3.4, Revised 2011 10/16/2015 11:07 AM10/16/2015 11:07 AM10/16/2015 11:07 AM2

3. Steps for solving Real Life Linear Programming Problems 1.Solve a) List all of your restraints b) Determine your Objective Equation (usually dealing with Profit) c) Find the x -intercep t (y=0) and the y -intercept (x =0) Use Cover-up method to determine the intercepts d) Use Elimination/Substitution to determine the intersection points of the 2 equations 2.Check 10/16/2015 11:07 AM10/16/2015 11:07 AM10/16/2015 11:07 AM3

4. A grocer buys cases of almonds and walnuts. Almonds are packaged 20 bags per case. The grocer pays $30 per case of almonds and makes a profit of $17 per case. Walnuts are packaged 24 bags per case. The grocer pays $26 per case of walnuts and makes a profit of $15 per case. He orders no more than 300 bags of almonds and walnuts together at a maximum cost of $400. Use x for cases of almonds and y for cases of walnuts. Example 1 10/16/2015 11:07 AM10/16/2015 11:07 AM10/16/2015 11:07 AM4

5. Example 1 A grocer buys cases of almonds and walnuts. Almonds are packaged 20 bags per case. The grocer pays $30 per case of almonds and makes a profit of $17 per case. Walnuts are packaged 24 bags per case. The grocer pays $26 per case of walnuts and makes a profit of $15 per case. He orders no more than 300 bags of almonds and walnuts together at a maximum cost of $400. Use x for cases of almonds and y for cases of walnuts. X = Cases of Almonds Y = Cases of Walnuts 10/16/2015 11:07 AM10/16/2015 11:07 AM10/16/2015 11:07 AM5

6. Example 1 A grocer buys cases of almonds and walnuts. Almonds are packaged 20 bags per case. The grocer pays $30 per case of almonds and makes a profit of $17 per case. Walnuts are packaged 24 bags per case. The grocer pays $26 per case of walnuts and makes a profit of $15 per case. He orders no more than 300 bags of almonds and walnuts together at a maximum cost of $400. Use x for cases of almonds and y for cases of walnuts. X = Cases of Almonds Y = Cases of Walnuts (0, 0) (0, 12.5) Using Cover Up (13.3, 0) Using Cover Up (9, 5) Using Elimination 10/16/2015 11:07 AM10/16/2015 11:07 AM10/16/2015 11:07 AM6

7. A grocer buys cases of almonds and walnuts. Almonds are packaged 20 bags per case. The grocer pays $30 per case of almonds and makes a profit of $17 per case. Walnuts are packaged 24 bags per case. The grocer pays $26 per case of walnuts and makes a profit of $15 per case. He orders no more than 300 bags of almonds and walnuts together at a maximum cost of $400. Use x for cases of almonds and y for cases of walnuts. Example 1 verticesP= 17x + 15yProfit (0, 0)P = 17(0) + 15(0)P = 0 (0, 12.5)P = 17(0) + 15(12.5)P = $187.50 (13.3, 0)P = 17(13.3) + 15(0)P = $226.10 (9, 5)P = 17(9) + 15(5)P = $228 10/16/2015 11:07 AM10/16/2015 11:07 AM10/16/2015 11:07 AM7 X = Cases of Almonds Y = Cases of Walnuts

8. A grocer buys cases of almonds and walnuts. Almonds are packaged 20 bags per case. The grocer pays $30 per case of almonds and makes a profit of $17 per case. Walnuts are packaged 24 bags per case. The grocer pays $26 per case of walnuts and makes a profit of $15 per case. He orders no more than 300 bags of almonds and walnuts together at a maximum cost of $400. Use x for cases of almonds and y for cases of walnuts. Example 1 How many cases of almonds and walnuts maximize the grocer’s profit? The grocer should buy 9 cases of almonds and 5 cases of walnuts to have a maximum profit of $228. 10/16/2015 11:07 AM10/16/2015 11:07 AM10/16/2015 11:07 AM8 X = Cases of Almonds Y = Cases of Walnuts

9. A school is preparing a trip for 400 students. The company who is providing the transportation has 10 buses of 50 seats each and 8 buses of 40 seats, but only has 9 drivers available. The rental cost for a large bus is $800 and $600 for the small bus. Calculate how many buses of each type should be used for the trip for the least possible cost. Example 2 10/16/2015 11:07 AM10/16/2015 11:07 AM10/16/2015 11:07 AM9

10. Example 2 A school is preparing a trip for 400 students. The company who is providing the transportation has 8 small buses of 40 seats each and 10 big buses of 50 seats each but only has 9 drivers available. The rental cost is for $600 for the small bus and $800 for a large bus. Calculate how many buses of each type should be used for the trip for the least possible cost. X = Small Buses Y = Big Buses Small Buses Big Buses 10

11. Example 2 A school is preparing a trip for 400 students. The company who is providing the transportation has 8 small buses of 40 seats each and 10 big buses of 50 seats each but only has 9 drivers available. The rental cost is for $600 for the small bus and $800 for a large bus. Calculate how many buses of each type should be used for the trip for the least possible cost. X = Small Buses Y = Big Buses Small Buses Big Buses 11 (0, 9) Using Cover Up (5, 4) Using Elimination (0, 8) Using Cover Up

12. Example 2 A school is preparing a trip for 400 students. The company who is providing the transportation has 8 small buses of 40 seats each and 10 big buses of 50 seats each but only has 9 drivers available. The rental cost is for $600 for the small bus and $800 for a large bus. Calculate how many buses of each type should be used for the trip for the least possible cost. X = Small Buses Y = Big Buses 10/16/2015 11:07 AM10/16/2015 11:07 AM10/16/2015 11:07 AM VerticesC = 600x + 800yMax/Min (0, 8) (0, 9) (5, 4) VerticesC = 600x + 800yMax/Min (0, 8) C = 600(0) + 800(8) (0, 9) C = 600(0) + 800(9) (5, 4) C = 600(5) + 800(4) VerticesC = 600x + 800yMax/Min (0, 8) C = 600(0) + 800(8)$6,400 (0, 9) C = 600(0) + 800(9)$7,200 (5, 4) C = 600(5) + 800(4)$6,200 12