How To Solve Linear Programming Word Problems?

i know how to solve these problems but i dont know how to set up the inequalities
please help me in this problem
A builder has 60 lots on which she can build houses with one house on each lot. She builds 2 types of houses, colonial and ranch. Sales experiencing has taught her that she should plan to build at least 3 times as many ranch style houses as colonial. If she makes a profit of $5000 on each colonial and $4500 on each ranch, how many of each kind should she build to maximize profit?

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One Response to “How To Solve Linear Programming Word Problems?”

  1. Renie says:

    Let y= number of ranch and x= number of colonial:
    X>=0 and y>=0
    A builder has 60 lots on which she can build houses with one house on each lot.
    X+ y< =60 she should plan to build at least 3 times as many ranch style houses as colonial. Y>= 3x
    If she makes a profit of $5000 on each colonial and $4500 on each ranch, how many of each kind should she build to maximize profit?
    P= 5000X+ 4500y
    ——-
    The vertices are (0,0) , (0, 60) ,(15,45)
    Plug these in to find the largest P:
    I hope this helps!

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