A company produces a niche hunting blind. Because of the nature of this product, demand varies greatly by season. In fact, demand exceeds production capacity during hunting season (fall,) but is very low in the summer months. To meet the high demand during the fall, the company produces the blind year round, producing more than what is needed in the summer in order to carry over inventory into the peak season. Their production facility can produce at most 60 blinds per month using regular labor at a cost of $125 each. Up to 15 additional blinds can be produced by utilizing overtime labor at a cost of $135 each. The blinds are sold for $225. Because of storage cost and the opportunity cost of capital, each blind held in inventory from one month to the next incurs a cost of $15 per blind. Since demand is uncertain, the company would like to maintain an ending inventory of at least 5 blinds during the warm months (May–September) and at least 15 blinds during the other months (October–April). It is now the start of January and the company has 5 blinds in inventory. The forecast of demand over the next 12 months is shown in the following table. Formulate and solve a linear programming model in a spreadsheet to determine how many blinds should be produced each month to maximize total profit. Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec. 65 30 25 30 45 10 5 25 40 95 90 90
A company produces a niche hunting blind. Because of the nature of this product, demand varies greatly by season. In fact, demand exceeds production capacity during hunting season (fall,) but is very low in the summer months. To meet the high demand during the fall, the company produces the blind year round, producing more than what is needed in the summer in order to carry over inventory into the peak season. Their production facility can produce at most 60 blinds per month using regular labor at a cost of $125 each. Up to 15 additional blinds can be produced by utilizing overtime labor at a cost of $135 each. The blinds are sold for $225. Because of storage cost and the opportunity cost of capital, each blind held in inventory from one month to the next incurs a cost of $15 per blind. Since demand is uncertain, the company would like to maintain an ending inventory of at least 5 blinds during the warm months (May–September) and at least 15 blinds during the other months (October–April). It is now the start of January and the company has 5 blinds in inventory. The
| Jan. | Feb. | Mar. | Apr. | May | June | July | Aug. | Sept. | Oct. | Nov. | Dec. |
| 65 | 30 | 25 | 30 | 45 | 10 | 5 | 25 | 40 | 95 | 90 | 90 |
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