Answer :
- Partial Derivatives of 'x' ; ∂x/∂p = -2
- Partial Derivatives of 'y' ; ∂y/∂p = 8
Explain the term Partial Derivatives?
- Each partial derivative of a function with numerous variables can be found independently.
- This is due to the fact that we can only distinguish based on one individual variable at a time.
- In this process, we must treat other variables as coefficients or constants.
For the stated question;
- We can differentiate each of the functions with respect to p to find the necessary partial derivatives.
- We shall regard the second variable, q, as a constant.
x = 300 - 2p + 8q
Partial Derivatives of 'x' with respect to p is
∂x/∂p = -2
For ; y= 500 + 8p- 3q
Partial Derivatives of 'y' with respect to p is
∂y/∂p = 8
Thus,
- This demonstrates that, while brand A's demand declines as its price rises, brand B's demand rises in response to brand A's price increase.
- When the price is raised, the amount of growth in brand B's demand is greater than the level of decline in brand A's demand.
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The correct question is-
A supermarket sells two brands of granola: brand A at $p per pound and brand B at $q per pound. The daily demands x and y (in pounds) for brands A and B, respectively, are given by the following equations.
x= 300 - 2p + 8q and y= 500 + 8p- 3q
Find ∂y/∂p and ∂x/∂p and interpret the results.