A food factory makes three types of cereals, A, B and C, from a mix of several ingredients: Oates, Apricots, Coconuts and Hazelnuts. The cereals are packaged in 1 kg boxes. The following table provides details of the sales price per box of cereals and the production cost per ton (1000 kg) of cereals respectively. Sales price per box($) | Production cost per ton Cereal A 2.50 4.00 Cereal B 2.00 2.80 Cereal C 3.50 3.00. The following table provides the purchase price per ton of ingredients and the maximum availability of the ingredients in tons respectively. Ingredients | Purchase price ($) per ton | Maximum availability in tons Dates 100 10 Apricots 120 Coconuts 80 Hazelnuts 200 The minimum daily demand (in boxes) for each cereal and the proportion of the Oates, Apricots, Coconut and Hazelnuts in each cereal is detailed in the following table, Proportion of Minimum demand (boxes) Oates | Apricots | Coconuts| Hazelnuts Cereal A 0.8 0.1 0.05 0.05 Cereal B 700 0.65 0.2 0.05 0.1 Cereal C 750 0.5 0.1 0.1 0.3 a) Let rij 2 0 be a decision variable that denotes the number of kg of ingredient i, where i could be Oates, Apricots, Coconuts, Hazelnuts, used to produce Cereal j, here j is one of A. B,C, (in boxes). Formulate an LP model to determine the optimal production mix of cereals and the associated amounts of ingredients that maximises the profit, while satisfying the constraints. b) Solve the model in R/R Studio. Find the optimal profit and optimal values of the decision variables