Case Problem $3.$ Textile Mill Scheduling

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The Scottsville Textile Mill produces five different fabrics. Each fabric can be woven on one or more of the mill$$s $38$ looms. The sales department$$s forecast of demand for the next month is shown in Table $4\mathrm{.}16,$ 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: dobby 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 dobby and $30$ are regular. The rate of production for each fabric on each type of loom is given in Table $4\mathrm{.}17.$ The time required to change over from producing one fabric to another is negligible and does not have to be considered.

The Scottsville Textile Mill satisfies all demand with either its own fabric or fabric purchased from another mill. Fabrics that cannot be woven at the Scottsville Mill because of limited loom capacity will be purchased from another mill. The purchase price of each fabric is also shown in Table $4\mathrm{.}16.$

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Question:

a$.$Model$($about $1$ page for this case$),$ presenting in detail your $($linear programming in this case$)$ model.

b$.$Results$($length depends on the case$),$ presenting your results and answering the case$$s questions $($section in the statement of the case entitled $$Managerial Report$)$

c$.$ The$$Excel file used in your analysis