Suzie's Sweatshirts is a home-based company that makes upscale, hand painted sweatshirts for children. Forecasts of sales for the next year are
Each Shirt is sold for $15. The holding cost per shirt is 6% of the selling price per quarter. The shirts are painted by part-time workers who earn $4.50 per hour during the autumn. Because of the high demand for part-time help during the winter holiday season, labor rates are higher in the winter, and Suzie must pay the workers $6.00 per hour. In the spring, labor is more difficult to keep, and Suzie finds that she must pay $5.50 per hour to get qualified help. Each shirt takes 1.5 hours to complete.
Formulate the problem to a LP model to help Suzie plan production over the three quarters to minimize the combined production and inventory holding cost. Suppose there is no inventory at the beginning of the autumn.