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.

The maximal demand $($in tons$)$ for each product, the minimum cotton and wool propor$-$

tion in each product are as follows:

a$)$ Formulate an LP model for the factory that maximises the profit, while satisfying the

demand and the cotton and wool proportion constraints.

$[20$ Marks$]$

b$)$ Solve the model using R$/$R Studio. Find the optimal profit and optimal values of the

decision variables.

$[20$ Marks$]$

Hints:

Let $x_{ij}0$ be a decision variable that denotes the number of tons of products $j$ for

Bloom, $2=$ Amber, $3=$ Leaf $****$Note: Need Proper working r $-$ Programming code I tried my best but not getting any feasible solution.$*******$