Formulate this as LPP.












0












$begingroup$


A company has two grades of inspectors, I and II, who are to be assigned for a quality control inspection. It is required that at least $2000$ pieces be inspected per $8$ hour day. Grade I inspectors can check pieces at the rate of $50$ per hour with an accuracy of $97text{%}$. Grade II inspectors can check pieces at the rate of $40$ per hour with an accuracy of $95text{%}$. The wage rate of grade I inspector is $text{Rs. } 4.50$ per hour and that of grade II is $text{Rs. } 2.50$ per hour. Each time an error is made by an inspector , the cost to the company is $text{Rs. } 2.00$. The company has available for inspection job, $10$ grade I and $5$ grade II inspectors. Formulate the problem to minimize the total cost of inspection.






linear-programming operations-research







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$endgroup$












  • $begingroup$
    What have you tried? (-1) You may start by letting $n_1$ and $n_2$ to be the number of grade I and II inspectors and translate the word problem into the inequalities, such as $0 le n_1 le 10$, $0 le n_2 le 5$.
    $endgroup$
    – GNUSupporter 8964民主女神 地下教會
    Jan 9 '17 at 10:21










  • $begingroup$
    My formulation is minimize $z= 4.5*8*n_1+2.*8*n_2-2(50*8*3*n_1/100+40*8*5*n_2/100)$ subjected to 400*n_1+320*n_2>=2000 , n_1 <= 10, n_2 <=5
    $endgroup$
    – Isha Dhiman
    Jan 10 '17 at 5:13












  • $begingroup$
    Including your formulation in the question is better than in a comment, so that everyone who reads this question knows that you've done your work. I regret to say that I can't undownvote this question unless it's edited. When I read your question, I am not sure whether each inspector needs to work 8 hr/day, or he can work part-time.
    $endgroup$
    – GNUSupporter 8964民主女神 地下教會
    Jan 10 '17 at 9:16
















0












$begingroup$


A company has two grades of inspectors, I and II, who are to be assigned for a quality control inspection. It is required that at least $2000$ pieces be inspected per $8$ hour day. Grade I inspectors can check pieces at the rate of $50$ per hour with an accuracy of $97text{%}$. Grade II inspectors can check pieces at the rate of $40$ per hour with an accuracy of $95text{%}$. The wage rate of grade I inspector is $text{Rs. } 4.50$ per hour and that of grade II is $text{Rs. } 2.50$ per hour. Each time an error is made by an inspector , the cost to the company is $text{Rs. } 2.00$. The company has available for inspection job, $10$ grade I and $5$ grade II inspectors. Formulate the problem to minimize the total cost of inspection.






linear-programming operations-research







share|cite|improve this question











$endgroup$












  • $begingroup$
    What have you tried? (-1) You may start by letting $n_1$ and $n_2$ to be the number of grade I and II inspectors and translate the word problem into the inequalities, such as $0 le n_1 le 10$, $0 le n_2 le 5$.
    $endgroup$
    – GNUSupporter 8964民主女神 地下教會
    Jan 9 '17 at 10:21










  • $begingroup$
    My formulation is minimize $z= 4.5*8*n_1+2.*8*n_2-2(50*8*3*n_1/100+40*8*5*n_2/100)$ subjected to 400*n_1+320*n_2>=2000 , n_1 <= 10, n_2 <=5
    $endgroup$
    – Isha Dhiman
    Jan 10 '17 at 5:13












  • $begingroup$
    Including your formulation in the question is better than in a comment, so that everyone who reads this question knows that you've done your work. I regret to say that I can't undownvote this question unless it's edited. When I read your question, I am not sure whether each inspector needs to work 8 hr/day, or he can work part-time.
    $endgroup$
    – GNUSupporter 8964民主女神 地下教會
    Jan 10 '17 at 9:16














0












0








0


0



$begingroup$


A company has two grades of inspectors, I and II, who are to be assigned for a quality control inspection. It is required that at least $2000$ pieces be inspected per $8$ hour day. Grade I inspectors can check pieces at the rate of $50$ per hour with an accuracy of $97text{%}$. Grade II inspectors can check pieces at the rate of $40$ per hour with an accuracy of $95text{%}$. The wage rate of grade I inspector is $text{Rs. } 4.50$ per hour and that of grade II is $text{Rs. } 2.50$ per hour. Each time an error is made by an inspector , the cost to the company is $text{Rs. } 2.00$. The company has available for inspection job, $10$ grade I and $5$ grade II inspectors. Formulate the problem to minimize the total cost of inspection.






linear-programming operations-research







share|cite|improve this question











$endgroup$




A company has two grades of inspectors, I and II, who are to be assigned for a quality control inspection. It is required that at least $2000$ pieces be inspected per $8$ hour day. Grade I inspectors can check pieces at the rate of $50$ per hour with an accuracy of $97text{%}$. Grade II inspectors can check pieces at the rate of $40$ per hour with an accuracy of $95text{%}$. The wage rate of grade I inspector is $text{Rs. } 4.50$ per hour and that of grade II is $text{Rs. } 2.50$ per hour. Each time an error is made by an inspector , the cost to the company is $text{Rs. } 2.00$. The company has available for inspection job, $10$ grade I and $5$ grade II inspectors. Formulate the problem to minimize the total cost of inspection.






linear-programming operations-research




linear-programming operations-research






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Jan 9 '17 at 7:46









projectilemotion

11.4k62141




11.4k62141










asked Jan 9 '17 at 7:21









Isha DhimanIsha Dhiman

245




245












  • $begingroup$
    What have you tried? (-1) You may start by letting $n_1$ and $n_2$ to be the number of grade I and II inspectors and translate the word problem into the inequalities, such as $0 le n_1 le 10$, $0 le n_2 le 5$.
    $endgroup$
    – GNUSupporter 8964民主女神 地下教會
    Jan 9 '17 at 10:21










  • $begingroup$
    My formulation is minimize $z= 4.5*8*n_1+2.*8*n_2-2(50*8*3*n_1/100+40*8*5*n_2/100)$ subjected to 400*n_1+320*n_2>=2000 , n_1 <= 10, n_2 <=5
    $endgroup$
    – Isha Dhiman
    Jan 10 '17 at 5:13












  • $begingroup$
    Including your formulation in the question is better than in a comment, so that everyone who reads this question knows that you've done your work. I regret to say that I can't undownvote this question unless it's edited. When I read your question, I am not sure whether each inspector needs to work 8 hr/day, or he can work part-time.
    $endgroup$
    – GNUSupporter 8964民主女神 地下教會
    Jan 10 '17 at 9:16


















  • $begingroup$
    What have you tried? (-1) You may start by letting $n_1$ and $n_2$ to be the number of grade I and II inspectors and translate the word problem into the inequalities, such as $0 le n_1 le 10$, $0 le n_2 le 5$.
    $endgroup$
    – GNUSupporter 8964民主女神 地下教會
    Jan 9 '17 at 10:21










  • $begingroup$
    My formulation is minimize $z= 4.5*8*n_1+2.*8*n_2-2(50*8*3*n_1/100+40*8*5*n_2/100)$ subjected to 400*n_1+320*n_2>=2000 , n_1 <= 10, n_2 <=5
    $endgroup$
    – Isha Dhiman
    Jan 10 '17 at 5:13












  • $begingroup$
    Including your formulation in the question is better than in a comment, so that everyone who reads this question knows that you've done your work. I regret to say that I can't undownvote this question unless it's edited. When I read your question, I am not sure whether each inspector needs to work 8 hr/day, or he can work part-time.
    $endgroup$
    – GNUSupporter 8964民主女神 地下教會
    Jan 10 '17 at 9:16
















$begingroup$
What have you tried? (-1) You may start by letting $n_1$ and $n_2$ to be the number of grade I and II inspectors and translate the word problem into the inequalities, such as $0 le n_1 le 10$, $0 le n_2 le 5$.
$endgroup$
– GNUSupporter 8964民主女神 地下教會
Jan 9 '17 at 10:21




$begingroup$
What have you tried? (-1) You may start by letting $n_1$ and $n_2$ to be the number of grade I and II inspectors and translate the word problem into the inequalities, such as $0 le n_1 le 10$, $0 le n_2 le 5$.
$endgroup$
– GNUSupporter 8964民主女神 地下教會
Jan 9 '17 at 10:21












$begingroup$
My formulation is minimize $z= 4.5*8*n_1+2.*8*n_2-2(50*8*3*n_1/100+40*8*5*n_2/100)$ subjected to 400*n_1+320*n_2>=2000 , n_1 <= 10, n_2 <=5
$endgroup$
– Isha Dhiman
Jan 10 '17 at 5:13






$begingroup$
My formulation is minimize $z= 4.5*8*n_1+2.*8*n_2-2(50*8*3*n_1/100+40*8*5*n_2/100)$ subjected to 400*n_1+320*n_2>=2000 , n_1 <= 10, n_2 <=5
$endgroup$
– Isha Dhiman
Jan 10 '17 at 5:13














$begingroup$
Including your formulation in the question is better than in a comment, so that everyone who reads this question knows that you've done your work. I regret to say that I can't undownvote this question unless it's edited. When I read your question, I am not sure whether each inspector needs to work 8 hr/day, or he can work part-time.
$endgroup$
– GNUSupporter 8964民主女神 地下教會
Jan 10 '17 at 9:16




$begingroup$
Including your formulation in the question is better than in a comment, so that everyone who reads this question knows that you've done your work. I regret to say that I can't undownvote this question unless it's edited. When I read your question, I am not sure whether each inspector needs to work 8 hr/day, or he can work part-time.
$endgroup$
– GNUSupporter 8964民主女神 地下教會
Jan 10 '17 at 9:16










1 Answer
1






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oldest

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0












$begingroup$

$mathbf{text{Decision variable}}$



Let $x_1$ be No. of inspected items by Grade I inspector / $8$ hr



Let $x_2$ be No. of inspected items by Grade II inspector / $8$ hr



$mathbf{text{Subject to:}}$



$10 x_1 +5 x_2 ge 2000$



$x_1 le (50$ X $8) le 400$



$x_2 le (40$ X $8) le 320$



$x_1 ge 0$



$x_2 ge 0$



Minimise cost, $z$



$z=4.50$ X $0.97(10x_1)+2$ X $0.03(10 x_1)+2.50$ X $0.95(5x_2)+2$ X $0.05(5 x_2)$



$z=44.25 x_1 + 12.375 x_2$



I am new to LPP, but I think it has to go a bit in this direction. And next time you are posting a question, try to show your working so that we can share views.






share|cite|improve this answer









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    1 Answer
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    1 Answer
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    0












    $begingroup$

    $mathbf{text{Decision variable}}$



    Let $x_1$ be No. of inspected items by Grade I inspector / $8$ hr



    Let $x_2$ be No. of inspected items by Grade II inspector / $8$ hr



    $mathbf{text{Subject to:}}$



    $10 x_1 +5 x_2 ge 2000$



    $x_1 le (50$ X $8) le 400$



    $x_2 le (40$ X $8) le 320$



    $x_1 ge 0$



    $x_2 ge 0$



    Minimise cost, $z$



    $z=4.50$ X $0.97(10x_1)+2$ X $0.03(10 x_1)+2.50$ X $0.95(5x_2)+2$ X $0.05(5 x_2)$



    $z=44.25 x_1 + 12.375 x_2$



    I am new to LPP, but I think it has to go a bit in this direction. And next time you are posting a question, try to show your working so that we can share views.






    share|cite|improve this answer









    $endgroup$


















      0












      $begingroup$

      $mathbf{text{Decision variable}}$



      Let $x_1$ be No. of inspected items by Grade I inspector / $8$ hr



      Let $x_2$ be No. of inspected items by Grade II inspector / $8$ hr



      $mathbf{text{Subject to:}}$



      $10 x_1 +5 x_2 ge 2000$



      $x_1 le (50$ X $8) le 400$



      $x_2 le (40$ X $8) le 320$



      $x_1 ge 0$



      $x_2 ge 0$



      Minimise cost, $z$



      $z=4.50$ X $0.97(10x_1)+2$ X $0.03(10 x_1)+2.50$ X $0.95(5x_2)+2$ X $0.05(5 x_2)$



      $z=44.25 x_1 + 12.375 x_2$



      I am new to LPP, but I think it has to go a bit in this direction. And next time you are posting a question, try to show your working so that we can share views.






      share|cite|improve this answer









      $endgroup$
















        0












        0








        0





        $begingroup$

        $mathbf{text{Decision variable}}$



        Let $x_1$ be No. of inspected items by Grade I inspector / $8$ hr



        Let $x_2$ be No. of inspected items by Grade II inspector / $8$ hr



        $mathbf{text{Subject to:}}$



        $10 x_1 +5 x_2 ge 2000$



        $x_1 le (50$ X $8) le 400$



        $x_2 le (40$ X $8) le 320$



        $x_1 ge 0$



        $x_2 ge 0$



        Minimise cost, $z$



        $z=4.50$ X $0.97(10x_1)+2$ X $0.03(10 x_1)+2.50$ X $0.95(5x_2)+2$ X $0.05(5 x_2)$



        $z=44.25 x_1 + 12.375 x_2$



        I am new to LPP, but I think it has to go a bit in this direction. And next time you are posting a question, try to show your working so that we can share views.






        share|cite|improve this answer









        $endgroup$



        $mathbf{text{Decision variable}}$



        Let $x_1$ be No. of inspected items by Grade I inspector / $8$ hr



        Let $x_2$ be No. of inspected items by Grade II inspector / $8$ hr



        $mathbf{text{Subject to:}}$



        $10 x_1 +5 x_2 ge 2000$



        $x_1 le (50$ X $8) le 400$



        $x_2 le (40$ X $8) le 320$



        $x_1 ge 0$



        $x_2 ge 0$



        Minimise cost, $z$



        $z=4.50$ X $0.97(10x_1)+2$ X $0.03(10 x_1)+2.50$ X $0.95(5x_2)+2$ X $0.05(5 x_2)$



        $z=44.25 x_1 + 12.375 x_2$



        I am new to LPP, but I think it has to go a bit in this direction. And next time you are posting a question, try to show your working so that we can share views.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Jan 21 '17 at 8:03









        Tos HinaTos Hina

        1,037619




        1,037619






























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