282 Chapter 3 Systems of Linear Equations and Inequalities 61. Suppose Rick has 40 ft of fencing with which he can build a rectangular garden. Let x represent the length of the garden and let y represent the width. a. Write an inequality representing the fact that the total perimeter of the garden is at most 40 ft. b. Sketch part of the solution set for this inequality that represents all possible values for the length and width of the garden. (Hint: Note that both the length and the width must be positive.) 20 15 10 62. A manufacturer produces two models of desks. Model A requires 4 hr to stain and finish and 3 hr to assemble. Model B requires 3 hr to stain and finish and 1 hr to assemble.The total amount of time available for staining and finishing is 24 hr and for assembling is 12 hr. Let x represent the number of Model A desks produced, and let y represent the number of Model B desks produced. a. Write two inequalities that express the fact that the number of desks to be produced cannot be negative. b. Write an inequality in terms of the number of Model A and Model B desks that can be produced if the total time for staining and finishing is at most 24 hr. c. Write an inequality in terms of the number of Model A and Model B desks that can be produced if the total time for assembly is no more than 12 hr. 8 7 6 5 y 1 21 d. Graph the feasible region formed by graphing the preceding inequalities. e. Is the point (3, 1) in the feasible region? What does the point (3, 1) represent in the context of this problem? f. Is the point (5, 4) in the feasible region? What does the point (5, 4) represent in the context of this problem? 63. In scheduling two drivers for delivering pizza, James needs to have at least 65 hr scheduled this week. His two drivers, Karen and Todd, are not allowed to get overtime, so each one can work at most 40 hr. Let x represent the number of hours that Karen can be scheduled, and let y represent the number of hours Todd can be scheduled. (See Example 7.) a. Write two inequalities that express the fact that Karen and Todd cannot work a negative number of hours. b. Write two inequalities that express the fact that neither Karen nor Todd is allowed overtime (i.e., each driver can have at most 40 hr). c. Write an inequality that expresses the fact that the total number of hours from both Karen and Todd needs to be at least 65 hr. d. Graph the feasible region formed by graphing the inequalities. 65 60 55 45 40 35 30 25 20 15 e. Is the point (35, 40) in the feasible region? What does the point (35, 40) represent in the context of this problem? f. Is the point (20, 40) in the feasible region? What does the point (20, 40) represent in the context of this problem? 3 1 2 3 4 5 6 7 1 2 x 4 3 2 Model A desks Model B desks x y 50 5 5 10 15 20 25 30 35 40 45 50 55 60 65 10 Hours (Karen) Hours (Todd) x y 25 0 5 10 15 20 25 5 Width Length
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