The Brickhouse Company is planning to lease a fuel-efficient, hybrid delivery van for its northern sales territory. They can choose to lease the van under three alternative plans:

- Plan A - Brickhouse would pay \(\$ 0.34\) per kilometre and buy its own fuel.

- Plan B - Brickhouse would pay \(\$ 320\) per month plus \(\$ 0.10\) per kilometre and buy its own fuel.

- Plan C - Brickhouse would pay \(\$ 960\) per month, and the leasing company would pay for all fuel.

The leasing company will pay for all repairs and maintenance, insurance, registration and so on.

Fuel should cost \(\$ 0.06\) per kilometre.

Required:

Using kilometres driven as the units of volume, do the following:

a Write out the cost equation for the cost of operating the delivery van under each of the three plans.

b Graph the three cost equations on the same graph (put cost on the vertical axis and kilometres driven per month on the horizontal axis).

c Determine at what kilometres per month the cost of Plan A would equal the cost of Plan B.

d Determine at what kilometres per month the cost of Plan B would equal the cost of Plan C.

e Calculate the cost, under each of the three plans, of driving 3500 kilometres per month.