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Homework Help: Linear inequalities

  1. Nov 28, 2007 #1
    1. The problem statement, all variables and given/known data
    Mnimize and maximize:
    P=30x + 10y
    Subject to 2x + 2y > or = 4
    6x + 4y < or = 36
    2x + y < or = 10
    x, y > or = 0

    2. Relevant equations



    3. The attempt at a solution

    How would I go about graphing this on my calculator: 2x + 2y > or = 4. When I take out my ti-83 and try to input the equation 2x + 2y > or = 4 I can't seem to find how to put multiple variables into it and inout less than or equal to signs in there. I do realize how to do this pblem I just can't seem to grasp the idea of how to put it into a calculator. I would greatly appreciate all your help you can provide. Thanks.
     
  2. jcsd
  3. Nov 29, 2007 #2

    HallsofIvy

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    You CAN'T graph an inequality on a calculator. You can, however, graph the equation 2x+ 2y= 4 (solve for y and enter it as y= 2- x) and that is the boundary between "> 4" and "< 4". Since you have 5 inequalities, your "feasible" region will be the five sided figure bounded by those 5 lines. I'm sure that you know that the minimal and maximal values of your linear target function will occur at one of the 5 vertices of that region.
     
  4. Nov 30, 2007 #3
    Why use a calculator? Why not do it by hand? Don't be lazy! As HallsofIvy says, the 'feasible' region- the region that satisfies all inequalities- is the region bounded by all 5 lines. So plot the 5 lines by hand and find the bounded region. Then find all the points of intersection, see which point gives the lowest value for P= 30x + 10y- this will the minimisation of P, and the point that gives the highest value will be the maximum.
     
  5. Nov 30, 2007 #4

    HallsofIvy

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    What, do it the "old fashioned way? How primitive!

    Of course, if it easier to do it by hand than with a calculator...
     
  6. Dec 1, 2007 #5
    You can, but you have to choose the shaded area for yourself. Much easier to do so manually.
     
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