A grocers daily profit from the sale of two brands of cat fo

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

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.

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

Solution

a)

dP = (dP/dx).x + (dP/dy).y = (dP/dx)*1 + (dP/dy)*0 = (dP/dx) =

(80-8x+7y)-8(x-50)+4(y-20) =

(80-8*63+7*68)-8(63-50)+4(68-20) = 140 cents

b)

actual change = P(64,68) - P(63,68) =

[(64-50)(80-8*64+7*68)+(68-20)(57+4*64-7*68)] - [(63-50)(80-8*63+7*68)+(68-20)(57+4*63-7*68)] =

132 cents