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Problem 1. Production and Inventory Planning Model Surfs Up produces high-end surfboards. A challenge faced by Surfs Up is that their demand is highly seasonal. Demand exceeds production capacity during the warm summer months, but is very low in the winter months. To meet the high demand during the summer, Surfs Up typically produces more surfboards than are needed in the winter months and then carries inventory into the summer months. Their production facility can produce at most 50 boards per month using regular labor at a cost of $125 each. Up to 10 additional boards can be produced by utilizing overtime labor at a cost of $135 each. The boards are sold for $200. Because of storage cost and the opportunity cost of capital, each board held in inventory from one month to the next incurs a cost of $5 per board. Since demand is uncertain, Surfs Up would like to maintain an ending inventory (safety stock) of at least 10 boards during the warm months (May-September) and at least 5 boards during the other months (October- April). It is now the start of January and Surfs Up has 5 boards in inventory. The forecast of demand over the next 12 months is shown in the table below. Formulate and solve a linear programming model in a spreadsheet to determine how many surfboards should be produced each month to maximize total profit. Forecasted Demand Jan Feb Mar Apr May Jun July Aug Sep Oct Nov Dec 10 14 15 20 45 65 85 85 40 30 15 15