Do This Problem Right Now
description
Transcript of Do This Problem Right Now
Do This Problem Right Now
Given Find the minimum and maximum for equation,
0
0
2 8
2 2 4
x
y
x y
x y
2 3 .C x y
(0, 8)
(4, 0)
(0, 2)
(2, 0)
vertices C = 2x + 3y Min/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
04/20/2304/20/23 21:5021:50 11
LINEARPROGRAMMINGDay 2
Section 3.4, Revised 2011Section 3.4, Revised 2011
04/20/2304/20/23 21:5021:50 22
Steps for solving Real Life Linear Programming Problems
1. Solvea) List all of your restraintsb) Determine your Objective Equation (usually dealing with
Profit)c) Find the x-intercept (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
04/20/2304/20/23 21:5021:50 33
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
04/20/2304/20/23 21:5021:50 44
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 AlmondsY = Cases of Walnuts
0x
0
0
x
y
0
0
30 26 400
x
y
x y
0
0
30 26 400
20 24 300
x
y
x y
x y
17 15P x y
04/20/2304/20/23 21:5021:50 55
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 AlmondsY = Cases of Walnuts
0
0
30 26 400
20 24 300
x
y
x y
x y
17 15C x y (0, 0)
(0, 12.5)Using Cover Up
(13.3, 0) Using Cover Up
(9, 5) Using Elimination
04/20/2304/20/23 21:5021:50 66
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
17 15P x y
vertices P= 17x + 15y Profit
(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
04/20/2304/20/23 21:5021:50 77
X = Cases of AlmondsY = 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.
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.
04/20/2304/20/23 21:5021:50 88
X = Cases of AlmondsY = Cases of Walnuts
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
04/20/2304/20/23 21:5021:50 99
Example 2A 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
Bu
se
s
1010
0x0y
9x y 40 50 400x y
600 800C x y
Example 2A 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 BusesY = Big Buses
Small Buses
Big
Bu
se
s
1111
(0, 9)Using Cover Up
(5, 4) Using Elimination(0, 8)
Using Cover Up
0x0y
9x y 40 50 400x y
600 800C x y
Example 2A 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 BusesY = Big Buses
04/20/2304/20/23 21:5021:50
Vertices C = 600x + 800y Max/Min
(0, 8)
(0, 9)
(5, 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) 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
The school should rent 4 large buses and
5 small buses for the least possible cost of $6,200.
1212
0
0
9
40 50 400
600 800
x
y
x y
x y
C x y