Ye Olde-Fashioned Ice Cream Shoppe
The owners of Ye Olde-Fashioned Ice Cream Shoppe have a reputation in your community for producing the best tasting ice cream on earth. Their customers come from neighboring cities and towns, and visitors rarely pass through your community without stopping to sample the various ice cream flavors.
One of the secrets of their success is that they only use fresh dairy ingredients, which they purchase daily. Since there are now two stores in town, the Ice Cream Shoppe owners are trying to decide where they should purchase these ingredients. Overwhelmed with the data, they have approached you to help them make their decision.
Here is the information they have given you:
All ice cream at the Ice Cream Shoppe is made from two basic recipes, to which various flavors, fruits, nuts and candy are added to create a variety of tastes. One recipe is for their health conscious customers and is called “light” since it is less caloric than their “extra rich” recipe. A batch of “light” ice cream uses 1.5 dozen eggs, 2.5 gallons of cream, and 5.5 gallons of milk. A batch of “extra rich” ice cream uses 2 dozen eggs, 5 gallons of cream, and 3 gallons of milk. Both recipes require other ingredients, such as sugar, but these ingredients keep well and are not purchased daily.
The owners have recently collected data on how much ice cream they sell. They have noticed that the demand for their ice cream is higher on weekends and holidays. This data helped them make decisions regarding how many batches of each recipe they will need to make, on average, on different days. They have decided that on weekdays they need to make 6 batches of “light” ice cream and 10 batches of “extra rich.” On weekend days they need to make 6 batches of “light” ice cream and 12 batches of “extra rich.” They were surprised to find that on holidays they need to make 8 batches of “light” ice cream and 15 batches of “extra rich.”
The two stores in town charge different amounts for each ingredient. At Our Town Market eggs cost $1.25 per dozen, cream is $3.00 per gallon (although it is sold in pints and quarts), and milk is $2.75 per gallon. At Neighborhood Store eggs cost $1.15 per dozen, cream is $3.25 per gallon (also sold in pints and quarts), and milk is $2.60 per gallon. The owners of the Ice Cream Shoppe want to lock in these prices for the next year by signing a contract binding them to purchase ingredients exclusively at one store or the other.
One other detail you need to be aware of: if the owners follow the production plan outlined above, the demand is so great at Ye Olde Fashioned Ice Cream Shoppe that the store will sell all of its ice cream by the end of each day. Also, you may be interested to know that a gallon of “light” ice cream sells for $6.25, a gallon of “extra rich” ice cream sells for $7.50, and a batch of either type of ice cream makes 10 gallons.