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Math Help - Linear Programming revision Q.

  1. #1
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    Question Linear Programming revision Q.

    Dolly Trolleys manufacture trolleys for a chain of supermarkets. Demand for trolleys is buoyant, so all production can be sold. Two models are produced by Dolly - the streamline and the standard. The streamline has 3 wheels and the standard has 4 wheels. The daily availability of wheels is limited to 240. Dolly works a single 8-hour shift per day. There are 2 stages of manufacture for trolleys, fabrication an spraying. Spraying takes 24 minutes for each streamline trolley and 10 minutes for each standard, and frabrication takes 30 minutes for each streamline trolley and 20 minutes for each standard. three identical machines are available for fabrication, which can be used for either type of trolley(orboth). Spraying is carried out manually by one person per trolley, and there are two staff available for this process. The profit from seling a streamline trolley is 20 and for a standard trolley is 18. No more than 15 trolleys can be produced per hour because of storage limitations on work in progress.

    Solve how the above problem can be formulated as a linear programme and derive the optimal solution to the problem, calculating exact values for all your variables.



    Any help identifying and formulating the constraints?

    (s=streamline, r=standard)
    Wheel limitations: 3s + 4r (less than or equal) 240
    Labour : 54s + 30r (less than or equal) 480 (mins)

    What else? Are they correct?


    Thank you. (hopefully this is in the right section)
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  2. #2
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    In your labor constraint you did not take into account you have 3 machines for fabrication. You need one more constraint for storage.
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  3. #3
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    Quote Originally Posted by skyking View Post
    In your labor constraint you did not take into account you have 3 machines for fabrication. You need one more constraint for storage.
    What effect does the machines have on the equation? Can you show me?

    What affect does the 15 trolleys have on the 2 different types of trolleys:
    ????<=60(minutes)


    Thank you for the response.
    Stuck.
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  4. #4
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    Quote Originally Posted by iCONFUSED View Post
    What effect does the machines have on the equation? Can you show me?

    What affect does the 15 trolleys have on the 2 different types of trolleys:
    ????<=60(minutes)


    Thank you for the response.
    Stuck.
    Say it takes 30 minutes to fabricate one item and you have 3 machines to do that. How many items can you fabricate in 30 minutes? Now say you have 6 machines, will that change the number of items you can fabricate in 30 mintes?

    If you have a limitation on the number of items you can store per hour (15) and s,t represent the number of items you will manufacture per hour, you should have a constraint to represent that. i.e you should not manufacture more than 15 combined items (s+t) per hour.
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