Lagrange's Multipliers Homework

Directions: Write legibly and in pencil. Complete the homework on time and by yourself. For each problem, write the instructions, label the solution, show all steps, and write the final answer in a sentence. Do not turn in your scratch work. Staple your pages together, in the correct order, and use this page as a cover sheet.

(1) Use the method of Lagrange multipliers to maximize the function subject to

(2) Use the method of Lagrange multipliers to minimize the function subject to

(3)  Use the method of Lagrange multipliers to maximize the function subject to

(4)  Use the method of Lagrange multipliers to maximize the function subject to

(5) Use the method of Lagrange multipliers to minimize the function   subject to

(6) Use the method of Lagrange multipliers to minimize the function subject to

(7) Use the method of Lagrange multipliers with two parameters to minimize   subject to and

(8) Use the method of Lagrange multipliers with two parameters to minimize   subject to and

(9) Use the method of Lagrange multipliers with two parameters to minimize   subject to and

(10) Use the method of Lagrange multipliers with two parameters to maximize   subject to and

(11) A rectangular box with no top is to be constructed from of material. What should be the dimensions of the box if it is to enclose maximum volume?

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