Each of Exercises 61 through 68 involves either the chain rule for partial derivatives or the incremental approximation formula for functions of two variables.

A grocer’s daily profit from the sale of two brands of flavored iced tea is

cents, where x is the price per bottle of the first brand and y is the price per bottle of the second, both in cents. Currently the first brand sells for 70 cents per bottle and the second, for 73 cents per bottle.

a. Find the marginal profit functions, P_x and P_y.

b. Evaluate P_x and P_y for the current values of x and y.

c. Use calculus to estimate the change in daily profit that will result if the grocer decides to raise the price of the first brand by 1 cent and the price of the second by 2 cents.

d. Estimate the change in profit if the price of the first brand is increased by 2 cents and the price of the second is decreased by 1 cent.

Transcribed Image Text:

40)(554x + 5y) + (y - 45) (70 + 5x - 7y) P(x, y) = (x