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Math Help - Apps. of Linear Programming story problem

  1. #1
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    Apps. of Linear Programming story problem

    A manufacturer of tents makes a standard model and a lightweight model for distribution. Each standard tent requires 3 labor hours from the assembly department and 1 labor hour from the cutting department. Each lightweight tent requires 4 labor hours from the assembly department and 2 labor hours from the cutting department. The maximum labor hours available per day in the assembly and cutting departments are 84 and 32 respectively. If the company makes a profit of $45 on each standard model and $75 on each lightweight model, how many of each type of tent should be manufactured each day to maximize the total daily profit?


    - State the Objective Function: P= 45x+ 75y?

    - Linear Constraints: 3x+ 4y is less than or equal to 84?
    x+ 2y is less than or equal to 32?
    x is greater than or equal to zero?
    y is greater than or equal to zero?

    - State the corner points: ?

    - How many of each type of tent should be manufactured each day to maximize the total daily profit: ?




    I had a good start on this problem i think, but, then i got completely lost. Help would be much appreciated!!!! thank you
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  2. #2
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    You just about have it. x=# standard tents and y=# lightweight tents.

    You have 3x+4y\leq 84\Rightarrow y=\frac{-3}{4}x+21

    x+2y\leq 32\Rightarrow y=\frac{-1}{2}x+16

    These two lines intersect at x=20. You can graph and see.

    There are three vertex points: (0,21), (0,16), (20,6)

    Plug these into the profit equation and see which yields the max.
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  3. #3
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    Comment: what you have done makes no sense at all until you state that "x" is the number of standard tents produced each day and "y" is the number of lightweight tents produced each day.

    Yes, a person who is familiar with these types of problems can "guess" what you mean, as galactus did, but it is much better practice to clearly state what your variables represent. It also helps you keep track of what you are doing in complicted problems. And, finally, it would really shock your teacher!
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