Management ScienceLinear Program $/$Inventory ModelBarilla Pasta CaseBackground $($This case was taken from an article that appears in The Economist Nov. $2020)$Barilla Pasta is the largest pasta maker in the world. The organization has a modern high$-$tech facility located at its world headquarters in Parma, Italy. Barilla exports $60\%$ of its products; mainly to Europe and the U$.$S$.$ Because of the COVID pandemic, people around the world are staying home and cooking for themselves. As a result, pasta sales world wide have increased. Likewise, pasta sales for Barilla have increased around $30\%$ from $2019$ to $2020.$ One of Barilla's most important markets is Germany. Since March of $2020,$ Barilla has supplied $22\%$ of the pasta and $39\%$ of the pasta sauces and pestos eaten in Germany $($The Economist, Nov. $2020).$ Global sales for Barilla were $$4\mathrm{.}2$ billion for $2019.$The ProblemsBecause of the international growth in pasta sales, Barilla may be experiencing problems with its hourly production capacity and its rail $($train$)$ shipments. You are an executive with Barilla and you are a member of a team responsible for inventory and supply chains. You need to evaluate whether to focus your attention on hourly production capacity or rail car shipments as a way to increase revenue streams$\mathrm{.}1.$ Barilla has a total demand per ton shipment of $$22,982$ per day, and revenue $($sales$)$ per ton shipment for pasta $($X$)$ is $$11,497.$ The revenue per ton shipment for the pasta sauce and pesto $($X$)$ is $$11,485.$ Also, the production capacity that Barilla has available is $25$ tons per hour. It takes $20$ tons of capacity per hour to produce pasta and $4\mathrm{.}58$ tons of capacity per hour to produce the pasta sauces.Develop a linear program that will maximize the following daily revenue streams for Barilla, given that $$5,633,753$ is the daily revenue per shipment of pasta to Germany and $$1,263,452$ is the daily revenue for the sauces shipped to Germany.Note: The first problem involves managing