### Solve the linear model

##### Reference no: EM131408

Greater Ware Clothing, Inc. manufacturers and sells shirts and other apparel to retailers in the local area. Orders have been received and Greater Ware is interested in planning shirt production over the next two months. The following information has been gleaned from conversations with plant management:

At the beginning of month one, there are 75 shirts in inventory. Retailers have placed orders for 1300 shirts in month one and 1250 shirts in month two. Management insists that these orders are filled. Each shirt delivered to a retailer brings in \$12.75 in revenue. Management has requested that at least 50 shirts be kept in ending inventory due to sudden changes that can occur in ordering.

To make each shirt, 2.1 square yards of cloth are needed. There are currently 100 square yards of cloth in inventory. Up to 2800 square yards of cloth can be purchased each month for a cost of \$2.55 and \$2.70 per yard in month 1 and month 2 respectively. Cloth that is not used in one month can be stored and used in subsequent months.

Each shirt requires 30 minutes of labor time to produce. Current employment is expected to allow for up to 670 hours of labor in month one and 700 hours in month two. These figures cannot be altered by hiring more employees. The cost per hour for labor is \$9.30.

o All numbers above are available in an Excel data file.

o This is a linear model. If your model needs a different engine, then you need to rethink your approach to the model. Remember, there are no IF, Max, or MIN statements in linear models.

Aggressive sales by company representatives have generated additional demand. Demands figures for month one and two are now 1600 and 1750 shirts respectively. It is no longer possible to fill all demand orders each month. Modify your model (this will need additional decision cells to allow for the company to sell less than demand). Note that demand not filled in one month does not transfer to subsequent months (this will make things much easier). What are the apparent limiting resource constraints in your solution and in which period do they occur?

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