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Homework Help: Partial Derivatives used in a manufacturing scenario word problem

  1. Oct 19, 2011 #1
    1. The problem statement, all variables and given/known data
    A) if [PLAIN]http://www4d.wolframalpha.com/Calculate/MSP/MSP10819hf7feh5hf5hh7e00004ga728h1d42i6h0c?MSPStoreType=image/gif&s=18&w=161&h=20 [Broken]
    Find the partial derivatives?

    B) Suppose you are manufacturing blackboards and whiteboards and that P is your monthly profit when your selling price for a blackboard is $x and for a whiteboard is $y. compute dp/dy(50,25) and explain what your answer means in the context of this manufacturing scenario?

    3. The attempt at a solution

    partial derivatives part A)
    [PLAIN]http://www4d.wolframalpha.com/Calculate/MSP/MSP31819hf7fg47cd2027b00002b4b8bbei42a0a36?MSPStoreType=image/gif&s=34&w=196&h=36 [Broken]

    [PLAIN]http://www4d.wolframalpha.com/Calculate/MSP/MSP62719hf7f989cef27630000665714d1f4f917d4?MSPStoreType=image/gif&s=35&w=273&h=42 [Broken]

    Part B) substitute (50,25) into the partial derivative d/dy and explain what your answer means in the context of this manufacturing scenerio

    [PLAIN]http://www4b.wolframalpha.com/Calculate/MSP/MSP71819hf7fb0igibfd8h000068e7f2217hhi46eg?MSPStoreType=image/gif&s=7&w=269&h=43 [Broken]
    [PLAIN]http://www4b.wolframalpha.com/Calculate/MSP/MSP72219hf7fb0igibfd8h00004b0cd1cei6c98c94?MSPStoreType=image/gif&s=7&w=156&h=36 [Broken]

    I get a negative answer and I am not sure what this means in context of the manufacturing scenario.
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Oct 19, 2011 #2
    P=-13.93 would simply mean that your profit is $-13.93, which is a $13.93 loss.
     
  4. Oct 19, 2011 #3
    so substituting in (50,25) means that 50 blackboard ($x) and 25 whiteboards ($y) were sold and it was a monthly loss of 13.93$ ??
     
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