Kelloggs is selling Krave cereal. Each box costs $2.40 to produce. The regular price of a box of Krave is $4.50. There are 10,000 loyal consumers who will purchase a box each week regardless of whether the product is on sale or not. In addition, there are Switchers and Newbies. Switchers will purchase only if the product is on sale and their future purchase behavior is unaffected by past purchases. Newbies will also purchase only if the product is on sale. However, half of them will become loyal after an initial purchase. Each of these converted customers will generate a CLV of $25. The number of Switchers and Newbies will depend on the sale price according to the table below:

Price	# of Switchers	Number of Newbies
$4.50	0	0
$4.20	1000	200
$3.90	2000	400
$3.60	3000	600
$3.30	4000	800
$3.00	5000	1000
$2.70	6000	1200
$2.40	7000	1400

Note, all consumers pay the same price. For example, if the price is $3.90. Total unit sales will be 12,400 (10,000 loyals + 2000 switchers + 400 newbies). In addition, Kellogg will convert 200 newbies (1/2 of 400) into loyal customers, which generate an addition profit flow of $25 each.

1. If there is not a sale, i.e., Price = $4.50, what would be Kelloggs profit?

2. Suppose Kellogg decides to hold a sales promotion for Krave. Complete the table below to calculate the profit Kellogg would earn at each of the possible price points. Clearly indicate which price generates the largest profit.

Price	Quantity Sold	Net Margin	# of converted newbies	Total CLV of converted newbies	Profit
$4.20
$3.90
$3.60
$3.30
$3.00
$2.70
$2.40

Quantity Sold will be the total units sold at each price (including sales to loyals, switchers, and newbies). Net Margin = (Price Unit Cost) * Quantity Sold . # of converted newbies = (# of Newbies who purchase) /2. Total CLV of converted newbies = (# of converted newbies) * (CLV of each converted newbie). Profit = Net Margin + Total CLV of converted newbies.

3. Should Kellogg offer a sales promotion? If so, by how much will its profit increase? Hint: Compare the profit from 1) to the maximum profit obtainable in 2).

4. If the unit cost of producing a box of Krave increased (i.e., was larger than $2.40), do you expect the optimal price under a sales promotion would increase, decrease, or stay the same? Briefly explain why you think the price would change in that particular direction. Note, you do NOT need to calculate the optimal price or resulting profit.