Suppose it costs $20 to purchase one hour of labor and $10 to purchase one unit of capital. If L hours of labor and C units of capital are purchased then L-3/4C1/4 machines can be produced. There is a budget of $100 with which to purchase labor and capital. (a) Formulate an NLP to maxin'iiz-e the number of machines produced. Assume that the entire budget must be used and fractional machines can be produced. (we consider fractional machines \"work in progress\") (1)) Solve your model from part (a) using the Lagrange Multiplier Method and any other relevant optimization theory discussed in class. (c) Suppose the budget increases to $105. Use the Lagrange multiplier to estimate the change in the objective function value. ( Do NOT resolve the model to get the true solution or objective value.)