Problem:
The Backwoods General Store in Vermont sells a variety of outdoor clothing items and equipment, and several food products at its modern but rustic-looking retail store. Its food products include salmon and maple syrup. The store also runs a lucrative catalog operation. One of its most popular products is maple syrup, which is sold in metal half-gallon cans with a picture of the store on the front.
Maple syrup was one of the first products the store produced and sold, and it continues to do so. Setting up the syrup-making equipment to produce a batch of syrup costs $450. Storing the syrup for sales throughout the year is a tricky process because the syrup must be kept in a temperature-controlled facility. The annual cost of carrying a gallon of the syrup is $15. Based on past sales data, the store has forecasted a demand of 7,500 gallons of maple syrup for the coming year. The store can produce approximately 100 gallons of syrup per day during the maple syrup season, which runs from February through May.
Because of the short season when the store can actually get sap out of trees, it obviously must produce enough during this 4-month season to meet demand for the whole year. Specifically, store management would like a production and inventory schedule that minimizes costs and indicates when during the year they need to start operating the syrup-making facility full time on a daily basis to meet demand for the remaining 8 months.
Develop a syrup production and inventory schedule for The Backwoods General Store.