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URGENT: how do i solve this math word problem?

Published by: cfz 2009-01-09
  • An oil company operates two refineries which produce Regular, Midgrade, and Premium grades of gasoline. The Washington refinery costs $750,000 a day to operate. It produces 45,000 gallons of Regular, 30,000 gallons of Midgrade, and 60,000 gallons of Premium grade gasoline per day.
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    The Texas refinery $680,000 a day to operate. It produces 60,000 of Regular, 30,000 gallons of Midgrade, and 30,000 gallons of Premium grade gasoline per day. The oil company wants to produce gasoline at the following levels:
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  • First we call the numbers of days operating for Washington X en for Texas Y.

    Then the costs are calculated with C = 750,000 * X + 680,000 * Y
    The constraints are:
    45,000 * X + 60,000 * Y at least 900,000, but at most 1,800,000
    30,000 * X + 30,000 * Y at most 1,050,000
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    60,000 * X + 30,000 * Y at least 600,000

    Then you need to minimize the cost-formula while respecting the constraints.


  • washington refinery 20 days and the Texas refinery 15 days.


  • Your question is incomplete...


  • I think you can answer this problem.
    Assume refinery 1 is open for x day s and refinery 2 is open for y days
    Then
    Cost = 750,000x + 680,000y
    We also know from the number of gallons of each grade they need and how much they produce each day:
    Regular
    900,000<=45,000x + 60,000y and
    45,000x +60,000y <= 1,800,000
    which can be reduced to
    60<=3x+4y and
    3x+4y<= 120

    Mid grade
    30,000x+30,000y<=1,050,000
    which can be reduced to
    x+y<=35

    Premium
    600,000<=60,000x+30,000y
    which can be reduced to
    20<=2x+y


    So you are left with
    60<=3x+4y
    3x+4y<= 120
    x+y<=35
    20<=2x+y
    and your cost equation

    Now it gets a little messy so I wont do it out, but what you need to do is solve the cost equation for y, plug that into the four equations solve them for c and graph each one. To graph you assume it to be c=equation then on the graph you "shade" either over or under the line depending on whether it is less than or greater than c. Hopefully there should be a point that is shaded by all four equations that is the lowest possible c (yaxis) that is the lowest cost and that will also give you x days, use the cost equation to then solve for the y days






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