Question

The owner of a grocery store finds she can sell about 982 gallons of milk in a week if she prices it at $2.99 per gallon. If she drops the per-gallon price to $2.79, her weekly sales increase to about 1,204 gallons. Assuming a constant rate of change.

a. Find a model that gives weekly milk sales, in gallons, as a function of the per-gallon dollar price.
b. Predict this store owner's weekly milk sales if she sets the per-gallon price to $3.15. Only enter the number, in gallons, rounded to nearest integer.

Answer 1

• g = -1110p +4300.9
• 804 gallons

Explanation:

a) Price is the independent variable, so the data we are given can be written as ...

(price, gallons) = (2.99, 982) and (2.79, 1204)

Using the 2-point form of the equation for a line, we have ...

g = (g2 -g1)/(p2 -p1)(p -p1) +g1

g = (1204 -982)/(2.79 -2.99)(p -2.99) +982

g = -1110(p -2.99) +982 = -1110p +4300.9

g = -1110p +4300.9

__

b) When p = 3.15, the predicted sales volume is ...

g = -1110(3.15) +4300.9 = 804.4

Weekly sales are predicted to be 804 gallons at a price of $3.15.