A grocer\'s daily profit from the sale of two brands of cat food is P(x,y)=(x-50

Question

A grocer's daily profit from the sale of two brands of cat food is

P(x,y)=(x-50)(60-7x+8y)+(y-30)(41+8x-4y)

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 68 cents per can and the second for 61 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 second brand by one cent, but keeps the price of the first brand unchanged.

Answer: cents

b) What is the actual change in profit when the price is changed as in part (a)?

Answer: cents

Explanation / Answer

for marginal change we take partial derivative with respect to y

= (x-50)*8+(41+8x-4y)-4*(y-30)

so marginal change will be at x=68, y=62

=(68-50)*8+(41+8*68-4*62)-4*(62-30)

=353

for actual , profit at x=68, y=61

by putting in P(x,y)=(x-50)(60-7x+8y)+(y-30)(41+8x-4y)

= 11867

and at x=68, y=62

= 12224

chnge in profit = 12224-11867

=357

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