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The “Mill” produces five different fabrics. Each fabric can be wovenon one or more of the mill’s 38 looms. The sales department hasforecast demand for the next month. The demand data are shown in Table1.0, along with data on the selling price per yard, variable cost peryard, and purchase price per yard. The mill operates 24 hours a dayand is scheduled for 30 days during the coming month.The Mill has two types of looms: dobbie and regular. The dobbie loomsare more versatile and can be used for all five fabrics. The regularlooms can produce only three of the fabrics. The Mill has a total of38 looms: 8 are dobbie and 30 are regular. The rate of production foreach fabric on each type of loom is given in Table 1.1. The time tochange over from producing one fabric to another is negligible anddoes not have to be considered.The Mill satisfies all demand with either its own fabric or fabricpurchased from another mill. That is, fabrics that cannot be woven atThe Mill because of limited loom capacity will be purchased fromanother mill. The purchase price of each fabric is also shown in Table1.0.Table 1.0Monthly Demand, S

elling Price, Variable Cost, and Purchase Price Datafor The MillDemand Selling Price Variable Cost Purchase PriceFabric (yards) ($/yard) ($/yard) ($/yard)1 16,500 0.99 0.66 0.802 22,000 0.86 0.55 0.703 62,000 1.10 0.49 0.604 7,500 1.24 0.51 0.705 62,000 0.70 0.50 0.70Table 1.1Loom Production Rates for The MillLoom Rate (yards/hour)Fabric Dobbie Regular1 4.63 *2 4.63 *3 5.23 5.234 5.23 5.235 4.17 4.17* Fabrics 1 and 2 can be manufactured only on the dobbie loom.QuestionDevelop a model that can be used to schedule production for The Mill,and at the same time, determine how many yards of each fabric must bepurchased from another mill. Include a discussion and analysis of thefollowing items in your answer:1. The final production schedule and loom assignments for each fabric2. The projected profit3. A discussion of the value of additional loom time (The Mill isconsidering purchasing a ninth dobbie loom. What is your estimate ofthe monthly profit contribution of this additional loom?)4. A discussion of whether the objective of minimizing total costs may provide a different model than the objective of maximizing profit.