Exam 7: Multivariable Calculus

Solve the problem. -A company uses TV and magazines for advertising. They know that profit P is related to the amounts T spent on TV and M spent on magazines by the equation where P, M, and T are in hundreds Of thousands. Find the maximum profit.

Find the value. -Let . Find f(6, 6).

Evaluate. -

Find the value. -Find f(-3, 1, 5) for f(x, y, z) =

Provide an appropriate response. -Let R be the region bounded by the graphs of the equations Use set notation and double inequalities to describe R as a regular x region or regular y region, whichever is simpler.

Find the partial derivative. -Find fx for f(x, y) = 3 .

Solve the problem. -The Cobb-Douglas production function for a steel company is given by f(x, y) = 78x0.3y0.7 where x is the utilization of labor and y is the utilization of capital. If the company uses 1500 units of labor and 2200 units of Capital, how many units of steel will be produced? Round to the nearest whole unit.

Provide an appropriate response. -Find .

Provide an appropriate response. -Use Lagrange multipliers to maximize f(x, y, z) = 24x + 12y + 24z subject to

Evaluate the integral. -Evaluate the integral with the order reversed.

Solve the problem. -The number of cows that can graze on a ranch is approximated by C(x,y) = 9x + 5y - 4, where x is the number of acres of grass and y the number of acres of alfalfa. If the ranch has 30 acres of alfalfa and 25 acres of grass, how Many cows may graze?

Solve the problem. -Consider the data showing the average life expectancy of woman in various years. Find the regression line. Let the year 1900 represent x = 0.

Evaluate. -

Provide an appropriate response. -Find the local extrema for

Provide an appropriate response. -Find the least squares line for the points (4, 3), (6, 6), (8, 0), and (9, 9). Graph the data and the least squares line on the same axes.

Provide an appropriate response. -Find the average value of the function over the shaded region. f(x, y) = 9x + y

Find the value. -Find f(2, -1, 4) for f(x, y, z) =

Find the value. -Let Find f(4, 8).

Solve the problem. -The productivity of a petroleum company is given approximately by the function where x is the utilization of labor and y is the utilization of capital. If the company uses 1200 units of labor and 2100 units Of capital, how many units of petroleum will be produced? Round to the nearest whole unit.

Provide an appropriate response. -Maximize the product of two numbers if their sum must be 26.