Exam 8: Functions of Several Variables

The US Postal Service (USPS)will accept only packages with length plus girth no more than 102 inches. (See the figure.) What are the dimensions of the largest volume package the USPS will accept? Express your answer as an ordered triple in the form ( x,y,z ).

Find , where and R is the indicated domain. (Remember that you often have a choice as to the order of integration.)

Find , where and R is the indicated domain. (Remember that you often have a choice as to the order of integration.)

Find the volume under the graph of over the triangle and

Calculate when defined.

Evaluate for

Use the given tabular representation of the function to compute .

Your latest CD - ROM drive is expected to sell between units if priced at p . You plan to set the price between $100 and $400. What are the maximum and minimum possible revenues you can make? What is the average of all the possible revenues you can make? Please enter your answer as three numbers, separated by commas.

Your weekly cost (in dollars)to manufacture cars and trucks is given by Compute the marginal cost of manufacturing cars at a production level of 15 cars and 16 trucks. $ __________

Your weekly cost (in dollars)to manufacture x cars and y trucks is What is the marginal cost of a truck? Please enter your answer as a number without the units.

Graph the function.

The US Postal Service (USPS)will accept only packages with length plus girth no more than 108 inches. (See the figure.) What are the dimensions of the largest volume package the USPS will accept?

Your weekly cost (in dollars)to manufacture cars and trucks is given by Compute the marginal cost of manufacturing cars at a production level of 15 cars and 14 trucks.

The cost of controlling emissions at a firm goes up rapidly as the amount of emissions reduced goes up. Here is a possible model. where x is the reduction in sulfur emissions, y is the reduction in lead emissions (in pounds of pollutant per day), and C is the daily cost to the firm (in dollars)of this reduction. Government clean-air subsidies amount to $500 per pound of sulfur and $50 per pound of lead removed. How many pounds of pollutant should the firm remove each day to minimize the net cost (cost minus subsidy)? Enter your answer as an ordered pair in the form ( x, y ).

Locate the critical point of the function.

Calculate when defined. Enter your answers, separated by a comma.

or the function show cross section at .

Graph the function.

Evaluate for