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

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2 Answers

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.
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.

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