LINEARPROGRAMMING Day 2 Section 3.4 LINEARPROGRAMMING Day 2 8/23/2018 7:48 PM

Steps of Problem Solving Understand the problem Translate the problem Solve List all of your restraints Determine your Objective Equation (usually dealing with Profit) Use Cover-up to determine the intercepts Use Elimination/Substitution to determine the intersection points Check 8/23/2018 7:48 PM

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. 8/23/2018 7:48 PM

Example 1 X = Cases of Almonds Y = Cases of Walnuts 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 8/23/2018 7:48 PM

Example 1 X = Cases of Almonds Y = Cases of Walnuts 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, 12.5) Using Cover Up (9, 5) Using Elimination (0, 0) (13.3, 0) Using Cover Up 8/23/2018 7:48 PM

Example 1 X = Cases of Almonds Y = Cases of Walnuts vertices 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 vertices C = 17x + 15y Profit (0, 0) C = 17(0) + 15(0) C = 0 (0, 12.5) C = 17(0) + 15(12.5) C = $187.5 (13.3, 0) C = 17(13.3) + 15(0) C = $226.1 (9, 5) C = 17(9) + 15(5) C = $228 8/23/2018 7:48 PM

Example 1 X = Cases of Almonds Y = Cases of Walnuts 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 How many cases of almonds and walnuts maximize the grocer’s profit? 9 cases of almonds and 5 cases of walnuts help maximize the grocer’s profit. 8/23/2018 7:48 PM

Example 2 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. 8/23/2018 7:48 PM

Example 2 X = Small Buses Y = Big Buses 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   Big Buses     (0,9) (9,0)   (0,8) (10,0) Small Buses 8/23/2018 7:48 PM

Example 2 X = Small Buses Y = Big Buses 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 (0, 9) Using Cover Up Y = Big Buses Big Buses (0, 8) Using Cover Up (5, 4) Using Elimination Small Buses 8/23/2018 7:48 PM

Example 2 X = Small Buses Y = Big Buses Vertices C = 600x + 800y 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 Vertices C = 600x + 800y Max/Min (0, 8) C = 600(0) + 800(8) (0, 9) C = 600(0) + 800(9) (5, 4) C = 600(5) + 800(4) Vertices C = 600x + 800y Max/Min (0, 8) C = 600(0) + 800(8) (0, 9) C = 600(0) + 800(9) (5, 4) C = 600(5) + 800(4) Vertices C = 600x + 800y Max/Min (0, 8) (0, 9) (5, 4) $6400 $7200 $6,200 The school should rent 4 large buses and 5 small buses for the least possible cost of $6200 8/23/2018 7:48 PM