A firm has prepared the following binary integer program to evaluate a number of potentialnew capital projects. The firm's goal is to maximize the net present value of their decisionwhile not spending more than their currently available capital.Max 100x1 + 120x2 + 90x3 + 135x4s.t. 150x1 + 200x2 + 225x3 + 175x4 ≤ 500 {Constraint 1}x1 + x2 + x3 + x4 ≥ 2 {Constraint 2}x2 + x4 ≤ 1 {Constraint 3}x2 + x3 ≥ 1 {Constraint 4}x1 = x4 {Constraint 5}Which of the constraints ensures that at least two of the potential projects will be selected?A) Constraint 1B) Constraint 2C) Constraint 3D) Constraint 4E) Constraint 5

Consider the following integer linear programming model:Max Z = 5x1 + 6x2Subject to:17x1 + 8x2 ≤ 1363x1 + 4x2 ≤ 36x1, x2 ≥ 0 and integerWhat is the value of the objective function at the optimal solution?Hint: develop a simple integer programming model in Excel to solve this problem.

Consider the following linear program:minx1,x2,x3,x4c1x1+c2x2+c3x3+2x4subject to⎧⎩⎨x1+x2+x3+x4≥103x1+x2+4x3+2x4≥12x1≥0,x2≥0,x3≥0,x4≥0min𝑥1,𝑥2,𝑥3,𝑥4𝑐1𝑥1+𝑐2𝑥2+𝑐3𝑥3+2𝑥4subject to{𝑥1+𝑥2+𝑥3+𝑥4≥103𝑥1+𝑥2+4𝑥3+2𝑥4≥12𝑥1≥0,𝑥2≥0,𝑥3≥0,𝑥4≥0 The parameters c1,c2,c3𝑐1,𝑐2,𝑐3 are real numbers.(a) How many variables does the dual problem have? Answer 1 Question 2Suppose that the optimal solution to the primal is x1=0𝑥1=0, x2=0𝑥2=0, x3=0𝑥3=0, x4=10𝑥4=10.(b) What is the optimal value of the objective function of the dual linear program? Answer 2 Question 2.(c) How many entries of the optimal dual variable are equal to zero?

Modelling a fixed cost problem as an integer linear program requiresGroup of answer choicesadding the fixed costs in the objective function.using 0-1 variables.using multiple-choice constraints.using LP Relaxation.

Solving an integer programming problem by rounding off answers obtained by solving it as a linear programming problem (using Simplex LP), we find thatGroup of answer choicesThe values of decision variables obtained by rounding off are always very close to the optimal values.The value of the objective function for a maximization problem will likely be less than that for the Simplex LP solution.The value of the objective function for a minimization problem will likely be less than that for the Simplex LP solution.All constraints are satisfied exactly.

A feasible solution to an integer programming problem is ensured by rounding down non-integer solution values.Group of answer choicesTrueFalse