Question

A convenience store buys whole milk for $2.17 per gallon and sells it for $2.99 per gallon. It sells an average of 150 gallons per day. By tracking past changes in sales of whole milk with changes in sales of other grocery products, the manager has discovered that each one-gallon increase in the sales of whole milk is associated with a $1.00 increase in the sales of other grocery products. Every $1.00 increase in the sales of other grocery products yields a contribution margin of $0.38.

The manager is now considering a promotion where the price of whole milk will be lowered to $2.59 per gallon. If this past relationship between sales of whole milk and sales of other grocery products holds, by how many gallons must whole milk sales increase in order for the store to break even on this price promotion? Show your work.

Answer 1

Consider the given problem here the price of milk is “2.59 per gallon” and the new sales is “S1 gallon”. So, here the change of sales in gallon is “S1-150”. We have given that for every “$1” increase in sales of other grocery products yields a contribution margin of “$0.38”, => total yield is “0.38*(S1-150)”.

Now, we have to fig out the change in sales such that the store is in break even.

=> 0.38*(S1-150) = 2.99*150 - 2.59*S1= 448.5 - 2.59*S1.

=> 0.38*S1 - 57 = 448.5 - 2.59*S1, => 2.97*S1 = 505.5, => S1 = 505.5/2.97 = 170.2.

=> S1=170.2, => the increase in sale is given by “170.2 - 150 = 20.2 gallon”.