Question: Consider the following IP problem. Maximize z = 3 x 1 + 2 x 2 , subject to Constraint 1: 2 x 1 + 3

Consider the following IP problem.

Maximize z = 3x₁ + 2x₂,

subject to
Constraint 1:	2x₁+ 3x₂ 35,
Constraint 2:	3x₁ + x₂ 25,
Constraint 3:	x₁, x₂ 0,
Constraint 4:	x_1,x₂ = non-negative integer,

where x₁ and x₂ represent the decision variables. Solve this IP problem and answer the following questions.

a. What are the values of x₁ and x₂ at the optimal solution? What is the maximum value of z?

b.If the objective function coefficients change to z = 4x₁ + 3x₂, what are the values of x₁ and x₂ at the optimal solution? What is the maximum value of z?

c.Using the original objective function coefficients, if the first constraint changes to 2x₁ + 3x₂ 42, what are the values of x₁ and x₂ at the optimal solution? What is the maximum value of z?

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