ssume that the firm's operation is subject to the following production functionand price data:

= + =$=$

where X and Y are two variable input factors employed in the production of Q.

1. In theunconstrained case, whatlevels of X and Y will maximize Q?
2. It is possible to express the cost function associated with the use of X and Y in the production of Q asTC = 3X + 6Ysubject to the firm'sconstraintof anoperating budget of $25. Use theLagrange multiplier techniquetodetermine the optimal levels of X and Y.What is thefirm's total outputat these levels of input usage?What is the value of Lagrangian multiplier?
3. What will happen to thefirm's outputfrom amarginal increase in the operating budget? (Hint: This is another way of asking you to interpret the Lagrangian multiplier you found in B above).