Problem $3(40$ points$)$

Burlingham Mills produces denim cloth that it sells to jeans manufacturers. It is negotiating a contract with

Troy Clothing Company to provide denim cloth on a weekly basis. Burlingham has established its weekly

available production capacity for this contract to be between $0$ and $600$ yards, according to the following

probability density distribution:

$f(x)=\frac{x}{180000},0x600yd.$

Troy Clothing's weekly demand for denim cloth varies according to the following probability distribution:

Simulate Troy Clothing's cloth orders for $20$ weeks and determine the average weekly capacity and

demand. Also determine the probability that Burlingham will have sufficient capacity to meet demand.

$0\mathrm{.}5424593890\mathrm{.}6472920940\mathrm{.}5977047840\mathrm{.}9299570320\mathrm{.}6793239480\mathrm{.}1759637980\mathrm{.}4489581540\mathrm{.}1514954730\mathrm{.}6668991$

$0\mathrm{.}7656976550\mathrm{.}3038237180\mathrm{.}308737401($use this $)$ data to generate the production capacity you need$)$

$0\mathrm{.}087440447,0\mathrm{.}903425581,0\mathrm{.}706315973,0\mathrm{.}921392459,0\mathrm{.}289791314,0\mathrm{.}54874502,0\mathrm{.}862436306,0\mathrm{.}451239895$

$0\mathrm{.}8977400860\mathrm{.}1369885590\mathrm{.}6037958770\mathrm{.}0053810950\mathrm{.}1740656050\mathrm{.}8265310510\mathrm{.}8844775880\mathrm{.}9166010310\mathrm{.}996548042$

$0\mathrm{.}3171342210\mathrm{.}9326094160\mathrm{.}673235065($use this $20$Rand$()$ data to generate the weekly demand you need$).$ Please use it using Excel and upload relevant screenshots otherwise I will give negative vote.