Question 1201320: An oil company operates two refineries in a certain city. Refinery I has an output of 200, 100, and 100 barrels of low-, medium-, and high-grade oil per day, respectively. Refinery II has an output of 100, 200, and 600 barrels of low-, medium-, and high-grade oil per day, respectively. The company wishes to produce at least 1000, 1400, and 3000 barrels of low-, medium-, and high-grade oil to fill an order. If it costs $600/day to operate Refinery I and $900/day to operate Refinery II, determine how many days each refinery should be operated to meet the production requirements at minimum cost to the company.
Refinery I ? days
Refinery II ? days
What is the minimum cost?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! draw a table, such as the one shown below:
refinery 1 refinery 2
barrels of low grade oil per day 200 100 >= 1000
barrels of medium grade oil per day 100 200 >= 1400
barrels of high grade oil per day 100 600 >= 3000
cost to operate per day 600 900 minimize
variables x y
constraints
200x + 100y >= 1000
100x + 200y >= 1400
100x + 600y >= 3000
x >= 0
y >= 0
objective function
minimize 600x + 900y
graph the opposite of the constraints
feasible region is area on graph not shaded
find minimum cost at corner points.
graph is shown below:
minimum cost is at (2,6)
that would be refinery 1 operating for 2 days and refinery 2 operating for 6 days.
at that point:
cost is 600 * 2 + 900 * y = 6600 per day
low grade oil is 200 * 2 + 100 * 6 = 1000 barels a day
medium grade oil is 100 * 2 + 200 * 6 = 1600 barrels a day
high grade oil is 100 * 2 + 600 * 6 = 3800 barrels a day
all constraints are met at the minimum cost solutioon point.
you can evaluate the other points to see for yourself that their cost to operate per day is higher.
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