Question

Alpedo is considering opening stalls to sell ice cream on the 1KM long beach. It is estimated that there are 1000 sunbathers evenly spread along the beach and that each sunbather will buy one ice cream provided that they are priced at no more than $5. The effort of getting up from the sand to get an ice cream and return to the sun-bed is estimated at $0.5 for every 100m the sunbather is from a stall. Each ice cream costs $2 to Alpedo and it costs $25 per day to operate a stall no matter how many ice creams are sold.
Assuming that Alpedo wants to serve everybody how many stalls should it open? What would be the price per ice cream? How much profit would Alpedo make?

Answer 1

Consider the key figures - fixed cost per unit of operation is 25 and the cost to produce 1 ice cream is 2. The customers will pay no more than 5 and there are 1000 sunbathers each of whom will by one ice cream. The effort of getting up from sand and going back is 0.5 every 100 meters. Alpedo wants to serve everyone which is the key point. Everyone will buy only if the price is no more than 5. This will include the effort taken represented by 0.5 per 100 meters. So Alpedo should open more stalls such that the effort taken is less. For example, if therer is only 1 stall. It will be 1km away for some sunbathers as they are evenly spread for 1km. Hence for some, the effort will be zero and for others, it will be 5. Hence Alpedo should open more stalls. The effort is represented as per 100 meters. Alpedo can strategise and open 1 stall every 100 meter. It will then have to spend 25 per day for 11 stalls resulting in 275 as fixed cost. It can however charge upto 4.5 per ice cream as the effort is reduced to 0.5 for the sunbathers. Hence the price can be at 4.5. At this price, all the sunbathers will buy ice creams. Hence the total revenue will be 4500 (4.5*1000) To find the profit, subtract the cost. The firm will spend 2 every ice cream. Hence the variable cost is 2000 and the fixed cost is 275. Total cost is 2275. The profit is 4500 - 2250 = 2225. This is the optimum level as a lower stalls will increase the effort eating into the profits. If it opens 5 stalls spaced at 200m, then the effort will be 1. The fixed cost will be 5*25 = 125. The price can be only 4. tThe revenue is 4000 and the cost will be 2 per ice cream as 2000 + 125 = 2125. Profit will be 4000 - 2125 = 1875. Which is not optimum. Hence 10 is the perfect number of stalls and price will be 4.5 per ice cream and profit is 2225.