Assume that the firm's operation is subject to the following production function

and price data:

= +

= $ = $

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

A. In the unconstrained case, what levels of X and Y will maximize Q?

B. It is possible to express the cost function associated with the use of X and Y in the

production of Q as TC = 3X + 6Y subject to the firm's constraint of an operating budget

of $25. Use the Lagrange multiplier technique to determine the optimal levels of X and

Y. What is the firm's total output at these levels of input usage? What is the value of

Lagrangian multiplier?

C. What will happen to the firm's output from a marginal increase in the operating budget?

(Hint: This is another way of asking you to interpret the Lagrangian multiplier you found

in B above).