The “Mill” produces five different fabrics. Each fabric can be woven on one or more of the mill’s 38 looms …

       The “Mill” produces five different fabrics. Each   fabric can be woven   on one or   more of the mill’s 38 looms. The sales department has    forecast   demand for the next month. The demand data are shown in Table   1.0, along   with data on the selling price per yard, variable cost per    yard, and   purchase price per yard. The mill operates 24 hours a day    and is   scheduled for 30 days during the coming month.              The Mill has   two types of looms: dobbie and regular. The dobbie looms   are more   versatile and can be used for all five fabrics. The regular    looms can   produce only three of the fabrics. The Mill has a total of    38 looms: 8   are dobbie and 30 are regular. The rate of production for   each fabric   on each type of loom is given in Table 1.1. The time to    change over   from producing one fabric to another is negligible and    does not   have to be considered.                The Mill   satisfies all demand with either its own fabric or fabric    purchased   from another mill. That is, fabrics that cannot be woven at   The Mill   because of limited loom capacity will be purchased from    another   mill. The purchase price of each fabric is also shown in Table   1.0.                  Table 1.0         Monthly   Demand, Selling Price, Variable Cost, and Purchase Price Data   for The Mill                 Demand   Selling Price Variable Cost Purchase Price     Fabric   (yards) ($/yard) ($/yard) ($/yard)      1 16,500   0.99 0.66 0.80        2 22,000   0.86 0.55 0.70        3 62,000   1.10 0.49 0.60        4 7,500 1.24   0.51 0.70        5 62,000   0.70 0.50 0.70                 Table 1.1         Loom   Production Rates for The Mill                Loom Rate   (yards/hour)        Fabric   Dobbie Regular        1 4.63 *         2 4.63 *         3 5.23 5.23        4 5.23 5.23        5 4.17 4.17                 * Fabrics 1   and 2 can be manufactured only on the dobbie loom.             Question         Develop 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 be   purchased   from another mill. Include a discussion and analysis of the   following   items in your answer:                1. The final   production schedule and loom assignments for each fabric   2. The   projected profit        3. A   discussion of the value of additional loom time (The Mill is    considering   purchasing a ninth dobbie loom. What is your estimate of   the 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.     

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