A factory makes three products called Bloom, Amber, and Leaf, from three materials containing Cotton, Wool and
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Question:
A factory makes three products called Bloom, Amber, and Leaf, from three materials
containing Cotton, Wool and Nylon. The following table provides details on the sales
price, production cost and purchase cost per ton of products and materials respectively.
Sales price Production cost Purchase price
Bloom $ $ Cotton $
Amber $ $ Wool $
Leaf $ $ Nylon $
The maximal demand in tons for each product, the minimum cotton and wool proportion in each product are as follows:
Demand min Cotton proportion min Wool proportion
Bloom
Amber
Leaf
a Formulate an LP model for the factory that maximises the profit, while satisfying the
demand and the cotton and wool proportion constraints.
Marks
b Solve the model using RR Studio. Find the optimal profit and optimal values of the
decision variables.
Marks
Hints:
Let xij be a decision variable that denotes the number of tons of products j for
j in Bloom, Amber, Leaf to be produced from Materials i in CCotton,
WWool, NNylon
The proportion of a particular type of Material in a particular type of Product can be
calculated as:
eg the proportion of Cotton in product Bloom is given by: xC
xC xW x Please help me the R code for this question
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