C: ANSWERS TO SELECTED PROBLEMS

Chapter 7.1, Systems of Linear Inequalities

1. It is not a solution.

3. Draw a dashed line, slope –2, containing (0,0) and shade the half-plane on right side of line.

5. Draw a solid line, intercepts (0,5) and (–2,0), and shade the half-plane on right side of line.

7. Draw a vertical line, solid, through (0,0), and shade the half-plane on right side of line.

9. Corner point: . 11. Corner points: , (2,4), (4,4), (1,0), (4,0).

13. No corner points exist. 15. Corner points: (0,0), (0,5), (1,5), (6,0).

17. Corner points: (0,0), (0,5), (4,0), (2,3). 19. Corner points: (0,0), (0,7), (2,6), (5,2), (6,0).

21. Corner points: (0,9), (1,6), (6,1), (8,0). 23. Corner points: (0,9), (2,5), (5,1), (8,0).

25. Corner points: (0,9), (1,5), (3,2), (8,0). 27. Corner points: (0,3), (5,1/2), (5,–2), (0,–2).

29. No corner points, empty solution set.

Chapter 7.2, Finding an Optimal Value

1. Max = 10 at x = 2 and y = 2, Min = –14/3 at x = –4/3 and y = –2/3.

3. Max = 168 at x = 0 and y = 6, Min = 0 at x = 0 and y = 0.

5. Max = 152 at x = 7 and y = 0, Min = 32 at x = 0 and y = 4.

7. Max = 11 at x = 1 and y = 5. 9. Max = 22 at x = 2 and y = 3.

11. Max = 30 at x = 2 and y = 6. 13. Min = 22 at u = 6 and v = 1.

15. Min = 15 at a = 5 and b = 1.

17. Max = 7 at x = 5 and y = –2, Min = –3 at x = 0 and y = 3.

19. Max = 22/7 at x = 24/7 and y = –2/7, Min = –28/3 at x = 1/6 and y = 19/2.

Chapter 7.3, Solving Linear Programming Problems Graphically

1. Max = $3350, 25 chairs and 9.5 sofas. 3. Min = $75,000, 3750 of A and 2500 of B.

5. Max = 5156.25, 1875 A and 1875 B. 7. Max = $8,000, 80 corn and 160 oats.

9. Min = , soybean, oats. 11. Min = $520,000, 12 teachers and 8 aides.

Chapter 7.4, Chapter Review

1. Corner points: (0,9), (2,5), (5,1), (8,0). 3. Corner points: (0,2), (0,7), (6,2), (1,7).

5. Max = 36 at x = 10 and y = 0, Min = –12 at x = 2 and y = 0.

7. Min = at x = and y = . 9. Min = $138,000, 2500 tons A, 6000 tons B.

11. Min = $760 thousand, 31 A and 12 B.