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Name: Sec. No.

ID No.: Instr.

BIRLA INSTITUTE OF TECHNOLOGY & SCIENCE, PILANIFirst Semester, 2007-2008

Course No. AAOC C222 Quiz M.M. 40Course Title: Optimization Date: 21.09.2007 Time: 30 mts

Note: There are ten questions. Each correct answer carries 4 marksand wrong answer carries -1 marks. Write the most appropriate answerin the box provided below and nowhere else. Overwriting/cutting willbe treated as wrong answer.

Q. No. 1 2 3 4 5 6 7 8 9 10Ans.

D B C A B D C B D A

Q1 Consider the system2x1 − x2 + 4x3 − 2x4 + x5 = 6,x1 + x2 + 2x3 − x4 + x6 = 3The solution x2 = x4 = x5 = x6 = 0, x1 = x3 = 1 is(A) a basic solution (B) a basic feasible solution(C) a basic solution but not feasible (D) not a basic solution

Q2. Consider the following LPP:

Maximize z  = c1x1 + c2x2 + c3x3

subject to x1 − x2 + 2x3 ≤ 20

2x1 + x2 − x3 ≤ 10

x1 ≥ 0, x2 ≥ 0, x3 ≥ 0

The optimal solution yields the following objective equation

z + 8x1 + 3x4 + 4x5 = A where x4, x5 denote slack variables for the respectivefunctional constraints. Then A is(A) 190 (B) 100 (C) 120 (D) 160

Q3. Which statement is not true if a maximization problem has an unboundedsolution?(A) A data entry error has been made or a limiting constraint has been omitted.(B) The objective function value goes to +∞.(C) The values of all decision variables go to +∞.(D) The feasible region is unbounded

Q4. If the points (5, 5, 5) and (7, 9, 5) are both optimal solutions to a linear pro-gramming problem, what other point is also optimal?(A) (6, 7, 5) (B) (6, 7, 8) (C) (7, 5, 5) [D] (5, 9, 5)

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Q5. A ”non-binding” constraint is:(A) satisfied with an equality at the optimal solution

(B) not satisfied with an equality at the optimal solution(C) never a non-negativity variable constraint(D) none of the above

Q6 The functional constraints of a linear model with nonnegative variables are3x1 + 5x2 ≤ 16 and 4x1 + x2 ≤ 10. Which of the following points could notbe an optimal solution for the model?(A) x1 = 2.5, x2 = 0 (B) x1 = 0, x2 = 3.2(C) x1 = 2, x2 = 2 (D) x1 = 1, x2 = 2.25

Q7 Consider the following general form of a LPP

Maximize ProfitSubject to Amount of resource I used ≤ 50

Amount of resource II used ≤ 260 Amount of resource III used ≤ 150All decision variables (x1, x2) are non-negative.

The Z -row of the final table is Z +25s1 +40s3 = A (si are the slack variables).If the right hand side of constraint III is changed from 150 to 151, what wouldhappen to maximum possible profit?(A) It would be decreased by 25 (B) It would be decreased by 40(C) It would be increased by 40 (D) It would be increased by 25

Q8. If, in solving a linear programming minimization problem using the simplexmethod, a slack variable is given a positive coefficient in the objective function,this implies(A) there is a cost for using an amount of the resource greater than that whichis available.(B) there is a cost for failing to use the entire amount of the resource.(C)there is no cost for using the resource.(D) the resource can be substituted for another resource

Q9. Which property of linear programming models indicates that the decision vari-ables cannot be restricted to integer value and can take on any fractional value?(A) linearity (B) additivity (C) certainty (D)divisibility

Q10. Hong securities has $ 300,000 to invest in four stocks and three bonds.X 1, X 2, X 3, X 4 denote the amounts invested in each stocks and Y 1, Y 2, Y 3equal the amounts invested in each of the three bonds. Which of the followingshows that at least 40% of the investment in stocks must be in stock 1?(A) 0.6X 1 − .4(X 2 + X 3 + X 4) ≥ 0 (B)X 1 − .4(X 2 + X 3 + X 4) ≥ 0(C)) X 1 > 120000 (D) X 1 ≥ 0.4(X 2 + X 3 + X 4 + Y 2 + Y 3 + Y 4)