Read directions carefully. Provide everything that is asked for and show all work. given by: For...

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Read directions carefully. Provide everything that is asked for and show all work. given by: For a particular clothing company, the monthly cost in dollars to manufacture x sweaters and y shirts is C(x, y) = 3000 + 20x + 15y -0.02x²y. Compute the marginal cost of manufacturing one additional sweater when the current level of production is 10 sweaters (x = 10) and 20 shirts (y = 20). [8 points] Consider the following Optimization problem subject to the given constraint. z = f(x, y) = xy subject to 2x + y = 40. Use the method of Lagrange multipliers to find the maximum value. Express your answer as an ordered triple, (x, y, z). Box your final answer. [12 points] (Hint: You can also find the maximum using substitution to check your answer; however, you will only receive full credit with a complete Lagrange Multiplier solution.) 9. A function f(x, y) has the following partial derivatives: fx(x, y) = 3x + 2y - 10 fy(x, y) = 2x + 4y - 8 Find the critical point for the function. f(x,y). 10. Classify the critical point found in Problem #9 as Relative Minimum, Relative Maximum or Saddle point. (Hint: Use the Second Derivative Test.) Read directions carefully. Provide everything that is asked for and show all work. given by: For a particular clothing company, the monthly cost in dollars to manufacture x sweaters and y shirts is C(x, y) = 3000 + 20x + 15y -0.02x²y. Compute the marginal cost of manufacturing one additional sweater when the current level of production is 10 sweaters (x = 10) and 20 shirts (y = 20). [8 points] Consider the following Optimization problem subject to the given constraint. z = f(x, y) = xy subject to 2x + y = 40. Use the method of Lagrange multipliers to find the maximum value. Express your answer as an ordered triple, (x, y, z). Box your final answer. [12 points] (Hint: You can also find the maximum using substitution to check your answer; however, you will only receive full credit with a complete Lagrange Multiplier solution.) 9. A function f(x, y) has the following partial derivatives: fx(x, y) = 3x + 2y - 10 fy(x, y) = 2x + 4y - 8 Find the critical point for the function. f(x,y). 10. Classify the critical point found in Problem #9 as Relative Minimum, Relative Maximum or Saddle point. (Hint: Use the Second Derivative Test.)

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