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.