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Applied Finite Mathematics HW Solutions 14

Applied Finite Mathematics HW Solutions 14 - 12 EXERCISES...

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Unformatted text preview: 12 EXERCISES 1.4 . We graph the solution set for each inequality; the common region is the feasible set. For the inequality 23; + 33; 2 2, we first draw the line 29: + 33; = 2. Its a:- and yuinteroepts are 9: = 1 and y = 2/3. Since the test point (0,0) does not satisfy 2s + 33; 2 2, we shade out below the line (left figure below). The 93- and y-intercepts of the line 23: + y = 8 are a: = 4 and y = 8. Since the test point (0,0) satisfies 2s: + y S 8, we shade out above this line (right figure below). Feasible Sell ' x ('3) The inequalitiw a: Z 0 and y 2 0 require us to consider only points in the first quadrant, and on the positive 9:- and y-axas. We therefore shade out what remains of the seeond and fourth quadrants (left figure above). This shows the feasible _set. All of the vertices are obvious; they are shown in the right figure above. . We graph the solution set for each inequality; the common region is the feasible set. Fbr the inequality 29: + y 2 50, we first draw the line 29: + y = 50. Its a— and y—intercepts are a: = 25 and y = 50. Since the test point (0,0) does not satisfy 29: + y 2 50, We shade out below the line (left figure below). The a— and y—intercepts of the line 3 + 23; = 40 are a = 40 and y = 20. Sines the test point (0,0) does not satisfy 3+ 2y 2 40, we shade out below this line also (right figure below). . (441.0) x The inequalities a: 2 0 and y 2 0 require us to consider only points in the first quadrant, and on the positive 3- and y~axes. We therefore shade out what remains of the second and fourth quadrants (left figure above). This shows the feasible set. Two of the vertices are obvious. To find the third vertex, We solve for the point of intersection of the lines 23: + y = 50 and a + 2y : 40. If we substitute a: = 40 — 2y into 22: + y = 50, we obtain' This material has been reproduced in accordance whiz copyright law by [he lhiversity ofManitoba Bookstore. Further reproduction. in cart or in full. is 2111'qu mnhihilmi _.f'_"“. ...
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