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Find the ordered pair where the maximum value occurs for the equation C=12x-4y given the following constraints:

y>4
x>1
x+2y<16
y-x<5
 
Multiple choice:
A.(8,4)
B.(10,1)
C.(1,4)
D.(2,7)

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Andre W. | Friendly tutor for ALL math and physics coursesFriendly tutor for ALL math and physics ...
5.0 5.0 (3 lesson ratings) (3)
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I'm assuming your constraints contain ≤ and ≥, rather than < and >.
 
The expression (12x-4y) will be at a maximum when x is as large as possible and y is as small as possible. The smallest y can be is 4. Since x+2y≤16, the largest x can be is 8. Therefore, c=12x-4y has its maximum at (8,4), which is c=80.
William S. | Experienced scientist, mathematician and instructor - WilliamExperienced scientist, mathematician and...
4.4 4.4 (10 lesson ratings) (10)
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Valerie, I think the answer is D.  I did this by graphing the original equation and adding the constraints onto it, and I'm pretty sure D (2,7) is the answer.  I hope some other tutors on this site will weigh in with their answers.

Comments

Answer D does not satisfy the condition:
  Y - X< 5
 
   7 - 2 = 5
 
   I think the < , should have been ≤, because none of the answers will satisfy the constraints.