3. If is subject to f(x, y) = 7xy x² + y² - 14(x + y) = 49 find a global maximum stationary point and its value, a global minimum stationary point and its value as well as another stationary point that is neither a global maximum nor a global minimum.

I understand number 6 but not number 7

Hi, how can I tell if those stationary points are minimum, maximum or saddle?

Firm's production is represented by z=10x1/2y1/2. z=amount of output. x=amount of labor used. y=amount of capital used. Labor cost= 20 dollars per unit, Capital cost= 80 dollars per unit. Part a) 100 units are currently being made as the output. Labor's cost minimizing quantity=20. Capital's cost minimizing quantity=5. Draw a graph of this with both isocosts and isoquants. Part b) The business wants to make the output increase from 100 units to 140 units. In the short run, capital is fixed. What is the amount of labor needed? Show this in your graph in part a. Calculate the new total cost. Part c) In the graph from part a, draw and label a point that shows capital's and labor's cost minimizing level in the long run if the business wants to make 140 units.

Find the maximum and minimum values of the function f(x, y, z) = x²y²² subject to the constraint x² + y² +2²= 81. Maximum value is 27 occuring at (9, 9, 9) points (positive integer or "infinitely many"). points (positive integer or "infinitely Minimum value is -27 many"). occuring at (-9, -9, -9)