A coach company plans to purchase 30 coaches of three different types to carry 960 passengers. Depending on the type of coaches, the number of passengers that can be carried are 18, 24 and 42 respectively.

a) Use the Gauss-Jordan method to determine the number of buses of each type satisfying the preceding conditions.

b) The price for 18-passenger coaches is $180,000, for 24-passenger coaches is $220,000 and for 42-passenger coaches is $350,000 Determine the solution giving the minimum cost and find this cost.