Vin Rouge owns two wineries: Winery A can produce up to 300 bottles per day and Winery B can produce up to 200 bottles a day. It supplies wine to three bottle shops: Fig, Bear and Sky. Assume that every 10 bottles are packed into a box. Fig needs at most 20 boxes a day; Bear needs at least 18 boxes a day; and Sky needs only 5 boxes a day. The costs, associated with the delivery of each box of wine from the wineries to the bottle shops, are shown in the table below. All costs are given in dollars. Vin Rouge Fig Bear Sky Winery A 35 62 65 Winery B 28 36 32 (a) Why the scenario above can be modelled with a Linear Programming (LP) model? [5 Marks] (b) Formulate a linear programming (LP) model to determine a minimum cost delivery scheme that satisfies the need of the bottle shops and that does not exceed the production capacity of the wineries. [10 Marks] (c) Produce R code to solve the LP model in part (b). [5 Marks] (d) Solve the model in R/R Studio. Find the optimal cost and optimal values of the decision variables.