Question 1160123: 2. A factory makes three products called Spring, Autumn, and Winter, from three materials
containing Cotton, Wool and Silk. 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
Spring $60 $5 Cotton $30
Autumn $55 $4 Wool $45
Winter $60 $5 Silk $50
The maximal demand (in tons) for each product, the minimum cotton and wool proper-tion in each product is as follows:
Demand min Cotton proportion min Wool proportion
Spring 4800 55% 30%
Autumn 3000 45% 40%
Winter 3500 30% 50%
a) Formulate an LP model for the factory that maximizes the pro t, while satisfying the
demand and the cotton and wool proportion constraints.
b) Solve the model using R/R Studio. Find the optimal pro t and optimal values of the
decision variables.
Hints:
1. Let xij > 0 be a decision variable that denotes the number of tons of products
j for j 1 = Spring; 2 = Autumn; 3 = Winters to be produced from Materials
i = C=Cotton, W=Wool, S=Silk.
2. The proportion of a particular type of Material in a particular type of Product can be
calculated as:
e.g., the proportion of Cotton in product Spring is given by:
xC1
xC1 + xW1 + xS1
.
Answer by ikleyn(52812)   (Show Source):
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