Determine graphically the solution set for each system of ...
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Determine graphically the solution set for each system of inequalities and indicate whether the solution set is bounded or unbounded
24. 2x - y > 4
4x – 2y < -2
[pic]
No solution, because there is no intersection between areas.
28. x + y > 20
x + 2y > 40
x > 0, y > 0
[pic]
Blue area denotes the intersection or the solution of systems of inequalities.
Region is unbounded.
34. 6x + 7y < 84
12x – 11y < 18
6x – 7y < 28
x > 0, y > 0
[pic]
Region is bounded.
Solve each linear programming problem by the method of corners.
14.
Maximize P = 2x + 5y
Subject to 2x + y < 16
2x + 3y < 24
y < 6
x > 0, y > 0
[pic]
Evaluate P at each corner.
P(0,6) = 2*0+5*6 = 30
P(3,6) = 2*3+5*6 = 36
P(6,4) = 2*6+5*4 = 32
P(8,0) = 2*8+5*0 = 16
So function is max at (3, 6) and max P = 36.
20.
Maximize C = 2x + 5y
Subject to 4x + y > 40
2x + y > 30
x + 3y > 30
x > 0, y > 0
[pic]
Region is unbounded. So, 2x+5y increases continuously. No optimal solution for maximum.
28.
Find the maximum and minimum of P = 4x + 3y Subject to
3x + 5y > 20
3x + y < 16
-2x + y < 1
x > 0, y > 0
• [pic]
Solve for P at each corner point.
P(15/13, 43/13) = (4*15/13) + (3*43/13) = 14.5385
P(3, 7) = 4*3+3*7 = 33
P(5, 1) = 4*5+3*1 = 23
So Maximum is P = 33 at x = 3 and y = 7
Minimum is P = 14.5385 at x = 15/13 and y = 43/13[pic]
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