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Thread: linear programing problem

  1. #1
    Jul 2010

    linear programing problem

    I'm a little confused about how to approach this problem..

    An appliance company produces 3 models of stoves. Model A takes 24 hours to manufacture and 20 hours to assemble. Model B take 15 hours to manufacture and 4 hours to assemble. Model C takes 9 hours to manufacture and 12 hours to assemble. The company can spend no more than 3000 hours on manufacturing and no more than 3200 on assembly. the profit for Model A is $120 per stove, Model B is $70 per stove, Model C is $50 per stove. How many of each model should the company produce to maximize profit? What is the maximum profit?

    I think simplex can be used to approach this problem, however when i set up the matrix I only get 2 equations and the equation to be maximized. Is this possible to solve with only two equations, and 3 variables?

    i set up the equations:
    maximize: 120x+70y+50z=p
    subject to: 24x+15y+9z<or=3000 ; 20x+4y+12<or=3200

    when i use the simplex method i get c= 16,000 in the last row. is this method right?

    does this have a solution?

    If anyone can help me get this set up or tell me what im doing wrong it will be greatly appreciated. thanx!
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  2. #2
    A Plied Mathematician
    Jun 2010
    CT, USA
    Well, I just used the Excel Solver routine, and it gave me x = 0, y = 50, and z = 250. The maximum profit computed is $16,000. So I would double-check your Simplex method implementation - you probably made an error somewhere. I do think this problem has a solution.
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