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. Newsletter #81:: communities throughout this country is an issue as urgent as the lack math problem should take more than five minutes to solve, and if a problem takes http://www.math.washington.edu/~warfield/news/news81.htmlHOME |
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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
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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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