Is my LP model correct?

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A Digital Image Printing (DIP) company makes two types of printers: industrial and home printers. The company makes P400 profit from each industrial and a P200 profit from each piece of home printer. The company has a contract to provide a store with exactly 30 printers per month. A separate industrial company supply DIP with at least 80 printer heads per month. DIP must purchase at least this amount but can order more. Each industrial printer requires 2 printer heads; each piece of home printer requires 8 printer heads. From past performance, the shop owners know they cannot make more than 20 industrial printers per month. They want to know the number of printers of each type to produce in order to maximize profit.




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linear-programming operations-research




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  • the question does not say how unused printer heads affect the profit
    – LinAlg
    Jul 16 at 14:47














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A Digital Image Printing (DIP) company makes two types of printers: industrial and home printers. The company makes P400 profit from each industrial and a P200 profit from each piece of home printer. The company has a contract to provide a store with exactly 30 printers per month. A separate industrial company supply DIP with at least 80 printer heads per month. DIP must purchase at least this amount but can order more. Each industrial printer requires 2 printer heads; each piece of home printer requires 8 printer heads. From past performance, the shop owners know they cannot make more than 20 industrial printers per month. They want to know the number of printers of each type to produce in order to maximize profit.




SOLUTION HERE




linear-programming operations-research




share|cite|improve this question





















  • the question does not say how unused printer heads affect the profit
    – LinAlg
    Jul 16 at 14:47












up vote
1
down vote

favorite









up vote
1
down vote

favorite












A Digital Image Printing (DIP) company makes two types of printers: industrial and home printers. The company makes P400 profit from each industrial and a P200 profit from each piece of home printer. The company has a contract to provide a store with exactly 30 printers per month. A separate industrial company supply DIP with at least 80 printer heads per month. DIP must purchase at least this amount but can order more. Each industrial printer requires 2 printer heads; each piece of home printer requires 8 printer heads. From past performance, the shop owners know they cannot make more than 20 industrial printers per month. They want to know the number of printers of each type to produce in order to maximize profit.




SOLUTION HERE




linear-programming operations-research




share|cite|improve this question














A Digital Image Printing (DIP) company makes two types of printers: industrial and home printers. The company makes P400 profit from each industrial and a P200 profit from each piece of home printer. The company has a contract to provide a store with exactly 30 printers per month. A separate industrial company supply DIP with at least 80 printer heads per month. DIP must purchase at least this amount but can order more. Each industrial printer requires 2 printer heads; each piece of home printer requires 8 printer heads. From past performance, the shop owners know they cannot make more than 20 industrial printers per month. They want to know the number of printers of each type to produce in order to maximize profit.




SOLUTION HERE





linear-programming operations-research





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edited Jul 16 at 8:00









Rodrigo de Azevedo

12.5k41751




12.5k41751









asked Jul 16 at 6:09









Manuel Garcia

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  • the question does not say how unused printer heads affect the profit
    – LinAlg
    Jul 16 at 14:47
















  • the question does not say how unused printer heads affect the profit
    – LinAlg
    Jul 16 at 14:47















the question does not say how unused printer heads affect the profit
– LinAlg
Jul 16 at 14:47




the question does not say how unused printer heads affect the profit
– LinAlg
Jul 16 at 14:47










1 Answer
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I have almost the same constraints except the following




A separate industrial company supply DIP with at least 80 printer
heads per month. DIP must purchase at least this amount but can order
more. Each industrial printer requires 2 printer heads; each piece of
home printer requires 8 printer heads




Since it is "at least" the constraint is $2x+8ygeq 80$.



There are several methods to solve such problems.



$1)$ You are lucky. This problem has only 2 variables. Thus it can be solved graphically. See here how it works. In this case the optimal solution is on the line $y=30-x$



$2)$ You can use a computer program. I have used the web page here. The formulation is



Maximize p = 400x+200y subject to 
x+y=30 
2x + 8y >= 80
x<= 20


Just mark, copy and paste it.



$3)$ It can be solved with the simplex method by yourself. If you want to apply this method and you have questions about it, feel free to ask.






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    1 Answer
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    up vote
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    I have almost the same constraints except the following




    A separate industrial company supply DIP with at least 80 printer
    heads per month. DIP must purchase at least this amount but can order
    more. Each industrial printer requires 2 printer heads; each piece of
    home printer requires 8 printer heads




    Since it is "at least" the constraint is $2x+8ygeq 80$.



    There are several methods to solve such problems.



    $1)$ You are lucky. This problem has only 2 variables. Thus it can be solved graphically. See here how it works. In this case the optimal solution is on the line $y=30-x$



    $2)$ You can use a computer program. I have used the web page here. The formulation is



    Maximize p = 400x+200y subject to 
    x+y=30 
    2x + 8y >= 80
    x<= 20


    Just mark, copy and paste it.



    $3)$ It can be solved with the simplex method by yourself. If you want to apply this method and you have questions about it, feel free to ask.






    share|cite|improve this answer

























      up vote
      0
      down vote













      I have almost the same constraints except the following




      A separate industrial company supply DIP with at least 80 printer
      heads per month. DIP must purchase at least this amount but can order
      more. Each industrial printer requires 2 printer heads; each piece of
      home printer requires 8 printer heads




      Since it is "at least" the constraint is $2x+8ygeq 80$.



      There are several methods to solve such problems.



      $1)$ You are lucky. This problem has only 2 variables. Thus it can be solved graphically. See here how it works. In this case the optimal solution is on the line $y=30-x$



      $2)$ You can use a computer program. I have used the web page here. The formulation is



      Maximize p = 400x+200y subject to 
      x+y=30 
      2x + 8y >= 80
      x<= 20


      Just mark, copy and paste it.



      $3)$ It can be solved with the simplex method by yourself. If you want to apply this method and you have questions about it, feel free to ask.






      share|cite|improve this answer























        up vote
        0
        down vote










        up vote
        0
        down vote









        I have almost the same constraints except the following




        A separate industrial company supply DIP with at least 80 printer
        heads per month. DIP must purchase at least this amount but can order
        more. Each industrial printer requires 2 printer heads; each piece of
        home printer requires 8 printer heads




        Since it is "at least" the constraint is $2x+8ygeq 80$.



        There are several methods to solve such problems.



        $1)$ You are lucky. This problem has only 2 variables. Thus it can be solved graphically. See here how it works. In this case the optimal solution is on the line $y=30-x$



        $2)$ You can use a computer program. I have used the web page here. The formulation is



        Maximize p = 400x+200y subject to 
        x+y=30 
        2x + 8y >= 80
        x<= 20


        Just mark, copy and paste it.



        $3)$ It can be solved with the simplex method by yourself. If you want to apply this method and you have questions about it, feel free to ask.






        share|cite|improve this answer













        I have almost the same constraints except the following




        A separate industrial company supply DIP with at least 80 printer
        heads per month. DIP must purchase at least this amount but can order
        more. Each industrial printer requires 2 printer heads; each piece of
        home printer requires 8 printer heads




        Since it is "at least" the constraint is $2x+8ygeq 80$.



        There are several methods to solve such problems.



        $1)$ You are lucky. This problem has only 2 variables. Thus it can be solved graphically. See here how it works. In this case the optimal solution is on the line $y=30-x$



        $2)$ You can use a computer program. I have used the web page here. The formulation is



        Maximize p = 400x+200y subject to 
        x+y=30 
        2x + 8y >= 80
        x<= 20


        Just mark, copy and paste it.



        $3)$ It can be solved with the simplex method by yourself. If you want to apply this method and you have questions about it, feel free to ask.







        share|cite|improve this answer













        share|cite|improve this answer



        share|cite|improve this answer











        answered Jul 16 at 14:14









        callculus

        16.4k31427




        16.4k31427






















             

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