The Cobb-Douglas function models the quantity q of a commodity produced as a function of the number of the workers w and the amount of capital invested c: q= 100w^0.1 C^0.9

Labor costs are $15 per worker, capital costs are $27 per unit, and there is a fixed budget of $3000. Set up (BUT DO NOT SOLVE!) the system of equations that would allow you to find the optimal values of w and c in order to maximize the quantity of a commodity produced.