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Math Help - [SOLVED] Use graphical methods to solve a linear programming problem

  1. #1
    Newbie majax79's Avatar
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    [SOLVED] Use graphical methods to solve a linear programming problem

    NVM
    Last edited by majax79; January 19th 2010 at 01:01 AM.
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  2. #2
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    Quote Originally Posted by majax79 View Post
    A math camp wants to hire counselors and aides 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 can accomodate 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?

    a. Define variables.
    b. Write a system of linear inequalities to model this problem.
    To a):

    s := monthly salary
    c := number of counselors
    a := number of aides

    to b):

    \left|\begin{array}{l}a+c \ge 30 \\<br />
a+c \le 45 \\<br />
a \ge 10 \\<br />
2c \le 3a\end{array} \right.<br />
Solve these inequalities vor c and draw the graphs. Determine the feasible polygon. Use the vertex which produces the lowest parallel to the line describing the salary.

    and:

    s = 2400 \cdot c + 1100 \cdot a

    I've got 30 aides and 0 counselors would cause the lowest costs.
    Attached Thumbnails Attached Thumbnails [SOLVED] Use graphical methods to solve a linear programming problem-monatskosten_camp.png  
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  3. #3
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    Quote Originally Posted by majax79 View Post
    Anyone?
    I'm just curious: What have you done during the last 3 hours? (beside typing "Anyone?")
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  4. #4
    Newbie majax79's Avatar
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    I've been working on this problem...oh and I masturbated too.
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  5. #5
    Master Of Puppets
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    Quote Originally Posted by majax79 View Post
    oh and I masturbated too.
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