Math 11 Embedded Assessment 1 Graphing Project
Page 21. We have determined that the profit objective function is P = 90x + 70y, where x is the number of games made at plant 1 and y is the number of games made at plant 2. The table of hours used at each plant activity has given us three constraints, 9x + y LTE 1700, 9x + 3y LTE 1800, and
4x + 8y LTE 2400.
1. On grid paper create axes in quadrant I with an x-scale of 600 and a y-scale of 1700.
2. Find easy points (0,y) and (x,0) for the three constraint boundaries.
9x + y = 1700, 9x + 3y = 1800, and 4x + 8y = 2400
You will get six easy points, two for each of the three lines.
3. Graph the three constraint boundaries using different colors.
4. Make estimates for the coordinates of the three intersections of the three lines. You will get three ordered pairs.
5. Take the constraint equations two at a time and use substitution or elimination to solve for x and y. You will get three ordered pairs.
6. Compare the results of 4. And 5.
7. On grid paper create axes in quadrant I with an x-scale of 400 and a y-scale of 400.
8. Look at the graph from 3. and look closely at the area where x < 400 and y < 400
9. Use the intercepts from 2. and the points from 5. to draw an enlarged graph on grid 7.
10. Shade the feasible region.
11. Identify the vertices.
12. Test the coordinates of the vertices in the profit function. This means substitute the coordinates of a vertex into P = 90x + 70y to get a value for P.
13. Determine which vertices or points give the greatest profit.
14. Explain what this means for manufacturing game systems.
The homework for Friday 9-16 is to work ahead and finish this project.
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