Section 3 4 LINEARPROGRAMMING Day 2 10272020 3

Steps of Problem Solving 1. Understand the problem 2. Translate the problem 3. Solve

Example 1 A grocer buys cases of almonds and walnuts. Almonds are packaged 20

Example 2 A school is preparing a trip for 400 students. The company who

Example 2 X = Small Buses Y = Big Buses (0, 8) Using Cover

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Section 3. 4 LINEARPROGRAMMING Day 2 10/27/2020 3: 21 AM 1

Steps of Problem Solving 1. Understand the problem 2. Translate the problem 3. Solve a) b) c) d) 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 4. Check 10/27/2020 3: 21 AM 2

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 10/27/2020 3: 22 AM 4

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. 10/27/2020 3: 22 AM 8

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. Big Buses X = Small Buses Y = Big Buses (0, 9) (9, 0) (0, 8) (10, 0) Small Buses 10/27/2020 3: 22 AM 9

Example 2 X = Small Buses Y = Big Buses (0, 8) Using Cover Up 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. (0, 9) Using Cover Up (5, 4) Using Elimination Small Buses 10/27/2020 3: 22 AM 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 Vertices C = 600 x + 800 y Max/Min (0, 8) C = 600(0) + 800(8) $6400 (0, 9) C = 600(0) + 800(9) $7200 (5, 4) C = 600(5) + 800(4) $6, 200 The school should rent 4 large buses and 5 small buses for the least possible cost of $6200 10/27/2020 3: 22 AM 11