The cost of converting a car to run on liquefied petroleum gas (LPG) is about K15,000 in Zambia, towards which a government grant would contribute about K7000. From September 1 2019, LPG will on average cost K7.5 per litre, compared with K 16 for ordinary unleaded petrol. However, LPG cars usually have slightly worse fuel consumption, losing about 13% in terms of Kilometers per Litre.

Fast-Trak company owns a fleet of 20 cars, which are bought new and are used for 30,000 Kilometres over two years before being sold off. The cars average 30 Kilometres to the Litre on petrol. The conversion to LPG does not affect the price in the secondhand market.

i). Calculate the profit contribution per hundred Kilomtres of LPG compared with unleaded petrol, for one of Fast-Trak's cars.

ii). Calculate the break-even mileage for the cars with the LPG conversion.

iii). Calculate the effect on the profit of Fast-Trak of converting to LPG.

iv). The government wants to encourage the use of LPG to protect the environment by reducing the break-even mileage to 10,000 Kilometres; how large a grant should it offer for the LPG conversion?