1 / 10

NCTM Standards: 1, 2, 6, 7, 8, 9, 10

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:.

aadi
Download Presentation

NCTM Standards: 1, 2, 6, 7, 8, 9, 10

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. NCTM Standards: 1, 2, 6, 7, 8, 9, 10

  2. Constraints: Limitation placed upon the variables.

  3. 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: Let x = the units of lumber produced Let y = the units of plywood produced. 6. Determine whether the situation calls for a maximum value or a minimum value & answer the question. 2. Write the constraints: x + y ≤ 600 x ≥ 150 y ≥ 225 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 3. Graph the system: 4. Write the profit equation:

  4. Infeasible Problem Ex: Ex: When the constraints of a linear programming problem cannot be solved simultaneously. The constraints do not define a region with any points in common. Unbounded The region formed is not a polygon. The graph has a minimum value at (5, 3), but there is no maximum value.

  5. Alternate Optimal Solutions When 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.

  6. Example 2 • Define the variables: Let b = # bookcases Let c = # of cabinets 2. Write the constraints: & the profit equation: Time available for woodworking: Time available for finishing: Two obvious ones we almost miss:

  7. $0 (0, 0) 60(0) + 40(0) $280 (0, 7) 60(0) + 40(7) $280 (2, 4) 60(2) + 40(4) $240 (4, 0) 60(0) + 40(0) 3. Graph the constraints: 4. Test the values in the profit equation: • Answer the question: The shop will make a maximum of $280 if they make 0 bookcases & 7 cabinets or 2 bookcases & 4 cabinets.

  8. Homework: Page 115

  9. Homework: Page 115

  10. Homework: Page 115

More Related