# Partial Derivatives used in a manufacturing scenario word problem

1. Oct 19, 2011

### Meow101

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. Oct 19, 2011

### frenchkiki

P=-13.93 would simply mean that your profit is $-13.93, which is a$13.93 loss.

3. Oct 19, 2011

### Meow101

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\$ ??