nctm standards: 1, 2, 6, 7, 8, 9, 10
DESCRIPTION
NCTM Standards: 1, 2, 6, 7, 8, 9, 10. Constraints: Limitation placed upon the variables. Example 1. 30(150) + 45(450)=. 24,750. 150, 450. 30(150) + 45(225)=. 150, 225. 14,625. 30(375) + 45(225)=. 21,375. 375, 225. 5. Substitute the values of the vertices:. 1. Define the variables:. - PowerPoint PPT PresentationTRANSCRIPT
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NCTM Standards: 1, 2, 6, 7, 8, 9, 10
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Constraints: Limitation placed upon the variables.
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Example 1
}){,(4530 profityxPyx
1. Define the variables:
Let x = the units of lumber produced
Let y = the units of plywood produced.2. Write the
constraints:x + y ≤ 600
x ≥ 150
y ≥ 2253. Graph the system:
4. Write the profit equation:
5. Substitute the values of the vertices:
150, 450
30(150) + 45(450)=
24,750
150, 225
30(150) + 45(225)=
14,625
375, 225
30(375) + 45(225)=
21,375
6. Determine whether the situation calls for a maximum value or a minimum value & answer the question. The mill wants
to maximize profit, so they should produce 150 units of lumber & 450 units of plywood for a maximum profit of $24,750
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Infeasible ProblemWhen the constraints of a linear programming problem cannot be solved simultaneously.
The constraints do not define a region with any points in common.
Ex:
UnboundedThe region formed is not a polygon. Ex:
The graph has a minimum value at (5, 3), but there is no maximum value.
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Alternate Optimal SolutionsWhen a linear programming application has two or more optimal solutions.This usually occurs when the graph of the function to be maximized or minimized is parallel to one side of the polygonal convex set.
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Example 2
701015 cb
365.49 cb
0
0
c
b
1. Define the variables:
2. Write the constraints: & the profit equation:Time available for woodworking:
Time available for finishing:
Two obvious ones we almost miss:
cbcb 4060),(Profit
Let b = # bookcases
Let c = # of cabinets
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701015 cb
365.49 cb
0
0
c
b
cbcb 4060),(Profit
3. Graph the constraints:
4. Test the values in the profit equation: (0,
0)60(0) + 40(0)$0
(0, 7)
60(0) + 40(7)$280
(2, 4)
60(2) + 40(4)$280 (4,
0)60(0) + 40(0)$24
0
5. Answer the question:The shop will make a
maximum of $280 if they make 0 bookcases & 7 cabinets or 2 bookcases & 4 cabinets.
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Homework: Page 115
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Homework: Page 115
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Homework: Page 115