math 11

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Please help this question is from my unit on linear programing and I'm having trouble completing it.
A company manufactures bicycles and tricycles. The total number of frames the company manufactures cannot exceed 80 per month. It takes the company 1 hour to assemble a bicycle and 2 hours to assemble a tricycle. The assembly machine is only available for 100 hours each month. If the company makes a profit of $50 on each bicycle and $70 on each tricycle, determine the number of bicycles and tricycles that will maximize profits each month. Indicate the maximum profit the company can make each month.
This is what I have so far: x=#of bicycles y=#of tricycles
x>=0 y>=0 P=50x +70y
Now I don't know what to do. Any help would be greatly appreciated. Thanks

  • math 11 -

    You need

    b+t </= 80 (frames limit)

    b + 2 t </= 100 (machine hour limit)

    graph those t on x axis, b on y axis

    they cross at
    (80-t)+2 t = 100
    t = 20
    b = 60
    look at resulting quadrilateral including axes, must be inside it

    so we have three realistic (t,b) points
    (0,80)
    (20,60)
    (50,0)
    check
    p = 70 t + 50 b
    at those three points
    which gives max p?

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