My Math Forum Simplex Word Problem (Linear Equation Issue)

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December 23rd, 2011, 07:57 AM   #1
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Simplex Word Problem (Linear Equation Issue)

Okay, we're having an issue with this problem, and even our teacher is confused on how the logic is on 1 of the equations.
So basically, the part in bold is the linear equation we're having trouble setting up.

Quote:
 A summer camp wants to hire counselors and aids to fill its staffing needs at minimum cost. The average monthly salary of a counselor is $2400 and the average monthly salary of an aide is$1100. The camp accommodate up to 45 staff members and needs at least 30 to run properly. They must have at least 10 aides, and may have up to 3 aides for every 2 counselors. How many counselors and how many aides should the camp hire to minimize cost?
The equation we're using for that in our simplex model is 3y <= 2x, but that causes the answer to be 18 counselors with 12 aides, but we know it's supposed to be 12 counselors with 18 aids.

What do you guys think?

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EDIT: Well we plugged in 2y <= 3x and got the correct answer. Anyone mind explaining the logic of the word problem and that linear equation?

 December 23rd, 2011, 02:06 PM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,933 Thanks: 1128 Math Focus: Elementary mathematics and beyond Re: Simplex Word Problem (Linear Equation Issue) x = aides, y = counselors. 30 ? x + y ? 45 x ? 10 3x ? 2y

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# how many counselors and how many sides should the camp hire to minimize cost

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