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Math Help - Linear programming problem.

  1. #1
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    Linear programming problem.

    A trucking firm ships containers of two companies, A and B. Each container from
    company A weighs 20 pounds and is 1 cubic foot in volume. Each container from company B weighs 30 pounds and is 3 cubic feet in volume. The trucking firm charges company A $1.50 for each container shipped, and charges company B $2.50 for each container shipped. The trucking company is obliged to load at least 250 containers from company A on each of its trucks, and each truck can carry no more than 21,000 pounds in weight and no more than 1500 cubic feet in volume.
    How many containers from companies A and B should a truck carry to maximize its revenue from shipping charges?
    Write down a mathematical model for the problem in the form of a linear program
    in standard form?

    So far Ive got: Let X1= # of containers from !, X2=# of containers from B

    LP:maximize p=1.5(X1)+2.5(X2)
    subject to: 20(X1)+30(X2) ≤ 21000
    X1+3(X2) ≤ 1500
    X1≥250
    X1,X2≥0
    I am just wondering If I have set everything up correctly?
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  2. #2
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    Re: Linear programming problem.

    Quote Originally Posted by farmeruser1 View Post
    A trucking firm ships containers of two companies, A and B. Each container from
    company A weighs 20 pounds and is 1 cubic foot in volume. Each container from company B weighs 30 pounds and is 3 cubic feet in volume. The trucking firm charges company A $1.50 for each container shipped, and charges company B $2.50 for each container shipped. The trucking company is obliged to load at least 250 containers from company A on each of its trucks, and each truck can carry no more than 21,000 pounds in weight and no more than 1500 cubic feet in volume.
    How many containers from companies A and B should a truck carry to maximize its revenue from shipping charges?
    Write down a mathematical model for the problem in the form of a linear program
    in standard form?

    So far Ive got: Let X1= # of containers from !, X2=# of containers from B

    LP:maximize p=1.5(X1)+2.5(X2)
    subject to: 20(X1)+30(X2) ≤ 21000
    X1+3(X2) ≤ 1500
    X1≥250
    X1,X2≥0
    I am just wondering If I have set everything up correctly? yes
    ...
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