A firm owns 2 plants. The cost function of the first plant is cA(yA) =3yA^2+ 2yA where yA is positive is the amount of output the first plant produces per month.

The second plant has the cost function cB(yB) = 2yB^2+ 2yB where yB is the amount of output the second plant produces per month. If the firm wishes to produce a total

amount y of output per month, how should it allocate it between the two plants to

minimize the total cost of production? Calculate the firm's cost function c(y).