A manufacturing process with a $12 million budget uses x kilograms of one raw material and y kilograms of a second raw material to make Q = 3 ln(x + 1) + 2 ln(y+1) units of product. The first raw material costs $6 million per kilogram and the second costs $3 million per kilogram.
(a) If the budget is fully spent, find an expression for y in terms of x. For what values of x does this expression make sense?
(b) Find the maximum number of units that can be produced under this budget.