Find the minimum value
Algebra
Level
2
Find the minimum value of the function 5x - 2y given that x+y >= 5 , x+y <= 10 ,0<=x<=10 and 0<=y<=10
25
50
-10
-20
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1 solution
This is a very simple Linear Programming problem that can be solved graphically or using elementary algebra. These two inequalities x+y >= 5 and x+y <= 10 form the feasible region for the solution. The minimum value of 5x - 2y will always fall on the extreme points of the feasible region so will fall on the vertices of the quadrilateral enclosed by the two inequalities x+y >= 5 and x+y <= 10. The four vertices (x,y) of the feasible region are (0,5); (5,0),(0,10);(10,0). The value of 5x - 2y is minimum at (0,10) which is equal to -20.