M&M is a company that makes knitted sweaters. Forecasts of sales for the next year are 150 in the autumn, 400 in the winter, and 50 in the spring. Plain sweaters are purchased from a supplier for $20.

The cost of capital is estimated to be 24% per year (or 6% per quarter); thus, the inventory holding cost per item is 0.06 × ( $20 ) = $1.20 per item in the ending inventory per quarter.

The company hires art students part - time to craft designs during the autumn, and they earn $5.50 per hour.

Because of the high demand for part - time help during the winter holiday season, labor rates are higher in the winter, and workers earn $7.00 per hour. In the spring, labor is more difficult to keep, and the owner must pay $6.25 per hour to retain qualified help.

Each sweater takes 2 hours to complete. We can hold about a maximum of 100 sweaters in house every quarter, if we need to hold more inventory then we can rent a warehouse which costs us $1.00 per item in the ending inventory per quarter. However, you cannot rent a warehouse unless the in-house warehouse in filled up.

There is maximum limit to the amount of inventory to be held in the rented warehouse.

Formulate as LP, setup and solve the problem in Excel. Please clearly specify your decision variables and define them properly.