Bestle A$.$S$.$ managers decide to produce and market a new cereal line called "Pops". The cereal will include four different types of components: Vitamin, Fiber, Protein, and Fat. Firstly, the marketing department conducted market research to understand customer requirements, As a result, Bestle decided to produce three different types of cereals for different customer segments: Pops Strong, Pops Fit and Pops Fun.

The cereals are produced by mixing four components. Experts from the R&D department determined some specifications on allowed percentages of components in each cereal type and presented them to managers as seen in Table $1.$ For example, the maximum percentage allowed for Vitamin in Pops Strong is $40\%,$ whereas it is $20\%$ for Pops Fit. Components are purchased in kilograms. After products are prepared, they are packaged with a conversion cost of $$0\mathrm{.}6$ per package. Each package has $0\mathrm{.}33kg$ capacity. The selling prices determined by the sales department are given in the last column of Table $1.$

Table $1.$ Compositions and Sales Prices of Different Cereals

$\backslash$table$[[$Cereal$,$Max Vitamins $\%,$Min Protein $\%,$Min Fiber $\%,$Max Fat $\%,\backslash$table$[[$Sales Price$],[($S$/$package$)]]],[$Strong$,40\%,25\%,20\%,25\%,8\mathrm{.}1],[$Fit$,20\%,20\%,15\%,15\%,6\mathrm{.}2],[$Fun$,30\%,15\%,10\%,30\%,6\mathrm{.}5]]$

At the second stage, procurement department of Bestle started surveying the supplier market for these components. After getting prices from many suppliers, two suppliers were determined to buy the components. Monthly availability of components and their costs are presented to the managers as in Table $2.$ Again for simplicity, assume that all components are purchased in $kg.$

Table $1.$ Compositions and Sales Prices of Different Cereals

$\backslash$table$[[$Cereal$,$Max Vitamins $\%,$Min Protein $\%,$Min Fiber $\%,$Max Fat $\%,\backslash$table$[[$Sales Price$],[($$$/$package$)]]],[$Strong$,40\%,25\%,20\%,25\%,8\mathrm{.}1],[$Fit$,20\%,20\%,15\%,15\%,6\mathrm{.}2],[$Fun$,30\%,15\%,10\%,30\%,6\mathrm{.}5]]$

At the second stage, procurement department of Bestle started surveying the supplier market for these components. After getting prices from many suppliers, two suppliers were determined to buy the components. Monthly availability of components and their costs are presented to the managers as in Table $2.$ Again for simplicity, assume that all components are purchased in $kg.$

$2$

Table $2.$ Capacities and Costs of Suppliers

$\backslash$table$[[,$Supplier $1,$Supplier $2],[$Component$,\backslash$table$[[$Monthly Available$],[$Amount $(kg)$ Formulate an LP model to determine the production plan of pops drinks for the next two months that maximizes the profit of Bestle. Report your decision variable, objective functiuon, and constraints in details.