Q2. A linear programming task is given: 

min (−6𝑥ଵ − 3𝑥ଶ)
subject to −𝑥ଵ − 4𝑥ଶ ≥ −12
8𝑥ଵ + 4𝑥ଶ ≤ 36
𝑥ଵ ≥ 0 , 𝑥ଶ ≥ 0

a)Transform the model in the standard form solvable by simplex method. How many new variables will be in the standard form?
b) Construct the initial simplex table and calculate the value of objective function for the first table.
c) Solve the task using the simplex method and write down the values of 𝑥ଵ and 𝑥ଶ in the optimal solution.
d) Calculate the interval of stability for the first cost coefficient 𝑐ଵ