partial derivatives

[eugenier]

hi, I Only Need Help With Part b. I got part a correct.

A grocer's daily profit from the sale of two brands of cat food is
P(x,y)=(x−70)(40−5x+8y)+(y−40)(40+3x−7y)
cents, where x is the price per can of the first brand and y is the price per can of the second, each in cents. Currently the first brand sells for 83 cents per can and the second for 84 cents per can.
a) Use marginal analysis to estimate the change in the daily profit that will result if the grocer raises the price of the first brand by one cent, but keeps the price of the second brand unchanged

part a is 364

What is the actual change in profit when the price is changed as in part (a)?
I couldn't solve this part, please, I need your help,

thanks

 

[Ishuda]

hi, I Only Need Help With Part b. I got part a correct.

A grocer's daily profit from the sale of two brands of cat food is
P(x,y)=(x−70)(40−5x+8y)+(y−40)(40+3x−7y)
cents, where x is the price per can of the first brand and y is the price per can of the second, each in cents. Currently the first brand sells for 83 cents per can and the second for 84 cents per can.
a) Use marginal analysis to estimate the change in the daily profit that will result if the grocer raises the price of the first brand by one cent, but keeps the price of the second brand unchanged

part a is 364

What is the actual change in profit when the price is changed as in part (a)?
I couldn't solve this part, please, I need your help,

thanks

Evaluate the profit function for x=83 and y=84. That is the current profit. Now evaluate the profit function for x=84 and y=84. That would be the profit if the price of the first brand was changed upward a penny. What is the difference?

 

[Deleted member 4993]

hi, I Only Need Help With Part b. I got part a correct.

A grocer's daily profit from the sale of two brands of cat food is
P(x,y)=(x−70)(40−5x+8y)+(y−40)(40+3x−7y)
cents, where x is the price per can of the first brand and y is the price per can of the second, each in cents. Currently the first brand sells for 83 cents per can and the second for 84 cents per can.
a) Use marginal analysis to estimate the change in the daily profit that will result if the grocer raises the price of the first brand by one cent, but keeps the price of the second brand unchanged

part a is 364

What is the actual change in profit when the price is changed as in part (a)?
I couldn't solve this part, please, I need your help,

thanks

\(\displaystyle \Delta P \ = \ \dfrac{\partial P}{\partial x} \Delta x \ + \ \dfrac{\partial P}{\partial y} \Delta y \)