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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=300â2p+8q y=500+8pâ3q Find âx/âp and ây/âp, and interpret the results.

Sagot :

  • 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,

  1. 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.
  2. 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.

To know more about the Partial Derivatives, here

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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.

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