Exam 15: Functions of Two or More Variables

Suppose that the production function for a product is , where x represents the number of work-hours and y represents the available capital (per week). Find the marginal productivity of x. ​

If the joint cost function for two products is (in dollars). Find the marginal cost with respect to y.

Suppose an area of land is to be sprayed with two brands of pesticide: x liters of brand 1 and y liters of brand 2. If the number of thousands of insects killed is given by . How many insects would be killed if 60 liters of brand 1 and 130 liters of brand 2 were used? Round your answer to the nearest integer. ​

Suppose that the joint cost function for two products is dollars. Find the marginal cost (function) with respect to x. ​

Suppose that a company's production for Q units of its product is given by the Cobb-Douglas production function , where K is dollars of capital investment and L is labor hours. Find Q if K = $8,600 and L = 640 hours. Round your answer to the nearest whole number. ​

Test for relative maximum and minimum. ​ ​

If , find . ​

Suppose that the joint cost function for two products is dollars. Find the marginal cost with respect to x. ​

Suppose that the total cost of producing 1 unit of a product is given by dollars, where x represents the cost per pound of raw materials and y represents the hourly rate for labor. The present cost for raw materials is $11 per pound and the present hourly rate for labor is $24. How will an increase of $1 per hour in labor costs affect the total cost? Round your answer to the nearest cent. ​

Test for relative maximum and minimum. ​ ​

Evaluate the function at the given values of the independent variables. ​ ​

If , find . ​

Suppose that the number of units of a good produced z is given by , where x is the number of machines working properly and y is the average number of work hours per machine. Find the production for a week in which 9 machines are working properly and the average number of work hours per machine is 35. Round your answer to the nearest whole number. ​

A company manufactures two products, A and B. If x is the number of thousands of units of A and y is the number of thousands of units of B, then the cost and revenue in thousands of dollars are ​ ​ Find the number of each type of product that should be manufactured to maximize profit. ​

If , find . ​

On the basis of past experience, a company has determined that its sales revenue (in dollars) is related to its advertising according to the formula , where x is the amount spent on radio advertising and y is the amount spent on television advertising. If the company plans to spend $30,000 on these two means of advertising, how much should it spend on each method to maximize its sales revenue? ​

The following table gives the actual or projected population in millions for a certain city for selected years from 2000 to 2050. Use linear regression to find the linear equation that is the best fit for the data, with x equal to the number of years past 2000. ​

If , find . ​

If , find . ​

Test for relative maximum and minimum. ​ ​