A factory would like to evaluate three raw materials (A, B, and C) of different sizes. The raw material needs to be stored in a warehouse. The total fixed cost for purchasing each type of raw materials is $1000, $2000, and $3000, respectively. The holding cost of each type of raw materials per unit is $30, $20, and $12, respectively.

a) Calculate the crossover point between material A and material B.

b) Calculate the crossover point between material B and material C.