Problem $5(20$ points$).$ A textile mill produces five types of fabrics. The demand $($in thousand

yards$)$ over a quarter$-$year time horizon for these fabrics is $16,48,37,23,$ and $82,$ respectively.

These five fabrics are woven, finished, and sold in the market at prices $0\mathrm{.}9,0\mathrm{.}8,0\mathrm{.}8,1\mathrm{.}2,$ and $0\mathrm{.}6$

$$/$per yard, respectively. Besides weaving and finishing the fabrics at the mill itself, the fabrics

are also purchased from outside sources and are then finished at the mill before being sold. If the

unfinished fabrics are purchased outside, the costs in $$/$per yard for the five fabrics are $0\mathrm{.}8,0\mathrm{.}7,$

$0\mathrm{.}75,0\mathrm{.}9,$ and $0\mathrm{.}7$ respectively. If produced at the mill itself, the respective costs are $0\mathrm{.}6,0\mathrm{.}5,0\mathrm{.}6,$

$0\mathrm{.}7,$ and $0\mathrm{.}3$ $$/$per yard. There are two types of looms that can produce the fabrics at the mill,

that is$,$ there are $10$ Dobbie looms and $80$ regular looms. The production rate of each Dobbie

loom is $4\mathrm{.}7,4\mathrm{.}6,5\mathrm{.}2,3\mathrm{.}8,$ and $4\mathrm{.}2$ yards per hour for the five fabrics. The regular looms have the

same production rates as the Dobbie looms, but they can only produce fabric types $3,4,$ and $5.$

Assume that the mill operates seven days a week and $24$ hours a day.

Formulate the problem of optimally planning to meet the demand over a quarter$-$year

horizon as a LO model. Use computer tools to find an optimal solution to this LO

model $($or report that it does not exist$).$ Please include all of your code in your submis$-$

sion