Question 85263: The minimum value of z = 4x + 10y subject to
3x + y (is less or equal to) 24
6x + 4y (is less or equal to) 66
x (is more or equal to) 0, y (is more or equal to) 0
is
A. 165
B. 110
C. 44
D. 32
Answer by scianci(186)   (Show Source):
You can put this solution on YOUR website! You need to test the extreme or "corner" points. These are (8 , 0) [8 is the biggest value x can be according to the first constraint, which in turn would make y = 0] , (0 , 24) [24 is the biggest value y can be according to the first constraint, which in turn would make x = 0] , (11 , 0) [11 is the biggest value x can be according to the second constraint, which in turn would make y = 0] , (0 , 16.5) [16.5 is the biggest value y can be according to the second constraint, which in turn would make x = 0]. Now, (0 , 24) doesn't conform to the second constraint and (11 , 0) doesn't conform to the first constraint, so they can be ruled out. So you need to plug in (8 , 0) and (0 , 16.5) into the expression 4x + 10y to get the respective values for z in each case:
4(11) + 10(0) = 44
4(0) + 10(16.5) = 165
44 is the smallest, so the answer is C.
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