Exam 8: Functions of Several Variables

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Calculate Calculate   . Choose the correct letter for each question.  . Choose the correct letter for each question. Calculate   . Choose the correct letter for each question.
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Solve the given problem by using substitution. Find the minimum value of Solve the given problem by using substitution. Find the minimum value of   subject to   . subject to Solve the given problem by using substitution. Find the minimum value of   subject to   . .

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For the function For the function   find   . Round to the nearest whole number if necessary. find For the function   find   . Round to the nearest whole number if necessary. . Round to the nearest whole number if necessary.

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For the function For the function   find   . find For the function   find   . .

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

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Compute the integral. Compute the integral.

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Cobb-Douglas productivity functions have the form Cobb-Douglas productivity functions have the form   where P stands for the number of items produced per year, x is the number of employees, and y is the annual operating budget. The numbers K and a are constants that depend on the situation we are looking at, with   How many items will be produced per year by a company that has 200 employees and an annual operating budget of $100,000 if K = 1,000 and a = 0.6? (Round your answer to one significant digit.) where P stands for the number of items produced per year, x is the number of employees, and y is the annual operating budget. The numbers K and a are constants that depend on the situation we are looking at, with Cobb-Douglas productivity functions have the form   where P stands for the number of items produced per year, x is the number of employees, and y is the annual operating budget. The numbers K and a are constants that depend on the situation we are looking at, with   How many items will be produced per year by a company that has 200 employees and an annual operating budget of $100,000 if K = 1,000 and a = 0.6? (Round your answer to one significant digit.) How many items will be produced per year by a company that has 200 employees and an annual operating budget of $100,000 if K = 1,000 and a = 0.6? (Round your answer to one significant digit.)

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Calculate Calculate   when defined.  when defined. Calculate   when defined.

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Your latest CD - ROM drive is expected to sell between Your latest CD - ROM drive is expected to sell between   units if priced at p . You plan to set the price between $300 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? units if priced at p . You plan to set the price between $300 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?

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Graph the function. Graph the function.

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Solve the given problem by using substitution. Minimize Solve the given problem by using substitution. Minimize   subject to   with   . subject to Solve the given problem by using substitution. Minimize   subject to   with   . with Solve the given problem by using substitution. Minimize   subject to   with   . .

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Evaluate Evaluate   for  for Evaluate   for

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Find the point on the given plane closest to (1,1,0). Find the point on the given plane closest to (1,1,0).   NOTE: Please enter your answer in the form ( x , y , z ). NOTE: Please enter your answer in the form ( x , y , z ).

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Calculate Calculate   when defined.  when defined. Calculate   when defined.

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Use Lagrange Multipliers to solve the problem. Find the maximum value of Use Lagrange Multipliers to solve the problem. Find the maximum value of   subject to   . subject to Use Lagrange Multipliers to solve the problem. Find the maximum value of   subject to   . .

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Calculate Calculate   when defined.  when defined. Calculate   when defined.

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Calculate Calculate   and evaluate them all at   . Choose the correct letter for each question.  and evaluate them all at Calculate   and evaluate them all at   . Choose the correct letter for each question.  . Choose the correct letter for each question. Calculate   and evaluate them all at   . Choose the correct letter for each question.
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Solve the given problem by using substitution. Find the minimum value of Solve the given problem by using substitution. Find the minimum value of   subject to   . subject to Solve the given problem by using substitution. Find the minimum value of   subject to   . .

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At what point on the given surface is the quantity At what point on the given surface is the quantity   a minimum? (The method of Lagrange multipliers can be used here.)  a minimum? (The method of Lagrange multipliers can be used here.) At what point on the given surface is the quantity   a minimum? (The method of Lagrange multipliers can be used here.)

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Your weekly cost (in dollars)to manufacture x cars and y trucks is Your weekly cost (in dollars)to manufacture x cars and y trucks is   What is the marginal cost of a car? What is the marginal cost of a car?

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