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Math Help - Need some help with a linear programming problem.

  1. #1
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    Question Need some help with a linear programming problem.

    Hope this is the correct section.

    Anyway I need some help from you fine folks.

    My problem:

    A call centre company has two types of employees - Sales and Service employees. The Company has office space for only 50 employees but there must always be at least 10 Sales and 12 Service employees on duty at one time. A sales employee wages are 9 per hour and service 6 per hour. The total hourly wage bill for all employees which the company can afford is limited to 360. The profit to the company for employing a Sales employee is estimated as 300 per hour and service 210 per hour.

    What I need to do is:
    A) formulate this information as a linear programming problem.

    B) Find the number of each employee type which the company should employ to maximise profit and calculate the profit.


    I only need help on part A as I just cannot wrap my head around these word problems

    Help much apreciated, thank's.

    Sorry if the section is wrong.
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  2. #2
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    Re: Need some help with a linear programming problem.

    Well, for starters you need an objective function. You're asked to maximise the profit, so the objective is to maximise the profit function. What is the profit function?
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  3. #3
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    Re: Need some help with a linear programming problem.

    Let's just say I have no idea how to do any of part A.
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    Re: Need some help with a linear programming problem.

    Quote Originally Posted by SirKillsalot View Post
    Let's just say I have no idea how to do any of part A.
    "The profit to the company for employing a Sales employee is estimated at $300 per hour and service $210 per hour."

    Well if \displaystyle P was your profit, \displaystyle x was the number of hours selling and \displaystyle y was the number of hours providing service, how could you write the above sentence as an equation?
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  5. #5
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    Re: Need some help with a linear programming problem.

    Well, a good start would be to answer Prove It's question!

    First step in any such problem- assign names to things. Let x be the number of sales employees and y be the number of service employees.

    "The Company has office space for only 50 employees but there must always be at least 10 Sales and 12 Service employees on duty at one time."

    So x+ y\le 50, x\ge 10, and y\ge 12.
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  6. #6
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    Re: Need some help with a linear programming problem.

    Well I have gotten as far as writing this on my own:

    x= Sales
    y= Service

    x>=10 x+y<=50
    y>=12
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  7. #7
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    Re: Need some help with a linear programming problem.

    Quote Originally Posted by SirKillsalot View Post
    Well I have gotten as far as writing this on my own:

    x= Sales
    y= Service

    x>=10 x+y<=50
    y>=12
    That's a good start. You also need to know which function to maximise (the profit function) that I mentioned earlier. You also have another constraint that is to do with how much money can be spent by the company. Can you write this constraint as an inequality?
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