6. Find the maximum rate of change of f(x, y) = x2y+exy sin y at (1,0). Answer :________

3. A manufacturer finds that it takes a units of labor and y units of capital to produce f(z,y) = 100x3/4y1/4 units of product. If a unit of labor costs $100, a unit of capital costs $200, and $200,000 is budgeted for production, determine how many units sbould be expended on labor and how many units should be expended on capital in order to maximize production.