Two additives, X1 and X2, can be used to increase the octane number of petrol. 1 kilogram of X1 in 5,000 litres of petrol increases the octane number by 10, while 1 kilogram of X2 in 5,000 litres increases the octane number by 20. The total additives must increase the octane number by at least 5, but a total of no more than 500 grams can be added to 5,000 litres, and the amount of X2 plus twice the amount of X1 must be at least 500 grams.

If X1 costs €30 a kilogram and X2 costs €40 a kilogram, formulate this problem as a linear programme. Use a graphical method to find an optimal solution.