An electrical company can produce electricity by burning 3 types of fuel. Burning a ton of each of the fuels produces different amount of power and releases a different amount of sulphur and other emissions in the atmosphere. The fuels can be combined in any proportion to obtain the optimal mixture. The company wants to minimise the price of the fuel, as well as the amount of sulphur in those fuels and the amount of emission from burning the fuel while producing 10000 MWatts of electricity.

Fuel type Sulphur Emission Price Mwatts 1 1200 3.2 50 300 2 1300 1.7 40 250 3 3500 2 60 350 What is the optimal value of Q if they consider minimisation of emissions three times more important than minimisation of price and sulphur? Hint: The answer to this question is between 0.46 and 0.51.

x1 - amount of fuel 1 to buy x2 - amount of fuel 2 to buy x3 - amount of fuel 3 to buy

40000 - target value for the amount of sulphur 57.14286 - target value for the amount of emission 1600- target value for the price

MIN: Q

(1200x1 + 1300x2 + 3500x3 - t1) / t1 <= Q 3 (3.2x1 + 1.7x2 + 2x3 - t2) / t2 <= Q (50x1 + 40x2 + 60x3 - t3) / t3 <= Q

300x1 + 250x2 + 350x3 = 10000

x1, x2, x3, Q >= 0