This is my answer for question is this correct,Please check and let me know

LP Model:

Let xC1, xW1, xN1 be the amount of cotton, wool, and nylon used for Bloom production (in tons).

Let xC2, xW2, xN2 be the amount of cotton, wool, and nylon used for Amber production (in tons).

Let xC3, xW3, xN3 be the amount of cotton, wool, and nylon used for Leaf production (in tons).

Objective:

The objective is to maximize profit, represented as:

Maximize: 60xC1 + 55xC2 + 60xC3 - 5xW1 - 4xW2 - 5xW3 - 40xN1 - 45xN2 - 30xN3

Constraints:

Demand:

xC1 + xW1 + xN1

xC2 + xW2 + xN2

xC3 + xW3 + xN3

Material Proportion:

xC1 / (xC1 + xW1 + xN1) >= 0.5 (for Bloom)

xW2 / (xC2 + xW2 + xN2) >= 0.6 (for Amber)

xW3 / (xC3 + xW3 + xN3) >= 0.3 (for Leaf)

Non-Negativity:

xC1, xW1, xN1, xC2, xW2, xN2, xC3, xW3, xN3 >= 0

b)

# Load the lpSolve library

library(lpSolve)

# Define the objective function

f.obj

# Define the constraints

f.con

0, 0, 0, 1, 1, 1, 0, 0, 0,

0, 0, 0, 0, 0, 0, 1, 1, 1,

1, 0, 0, 0, 1, 0, 0, 1, 0,

0, 0, 1, 0, 0, 1, 0, 0, 1),

nrow=5, byrow=TRUE)

dir.con =", ">=")

rhs.con

# Solve the LP problem

res

all.int=TRUE)#

# Print the optimal profit

res$objval

# Print the optimal values of the decision variables

res$solution

answer coming this

> # Print the optimal profit > res$objval [1] 252000

> > # Print the optimal values of the decision variables > res$solution [1] 4199 0 1 0 0 0 0 0 0

> > # Print the optimal values of the decision variables > res$solution [1] 4199 0 1 0 0 0 0 0 0

2. 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 proportion 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: 1. Let xij0 be a decision variable that denotes the number of tons of products j for j{1= Bloom, 2= Amber, 3= Leaf } to be produced from Materials i{C= Cotton, W= Wool, N=Nylon }. 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 Bloom is given by: xC1+xW1+xN1xC1