A Linear Programming Problem Contains a Restriction That Reads

MODULE B: LINEAR PROGRAMMING

TRUE/Faux

i. Linear programming helps operations managers brand decisions necessary to make effective utilize of resources such as machinery, labor, coin, fourth dimension, and raw materials.

Truthful (Introduction, easy)

ii. 1 requirement of a linear programming problem is that the objective function must exist expressed as a linear equation.

True (Introduction, piece of cake)

three. A mutual form of the product-mix linear programming seeks to find that combination of products and the quantity of each that maximizes profit in the presence of limited resources.

True (Formulating linear programming problems, moderate)

iv. Linear programming is an appropriate problem-solving technique for decisions that have no alternative courses of activity.

False (Requirements of a linear programming trouble, like shooting fish in a barrel)

five. In linear programming, a statement such every bit "maximize contribution" becomes an objective part when the trouble is formulated.

Truthful (Formulating linear programming problems, moderate)

6. Constraints are needed to solve linear programming bug by hand, but not past computer.

Simulated (Graphical solution to a linear programming trouble, like shooting fish in a barrel) {AACSB: Use of It}

seven. In terms of linear programming, the fact that the solution is infeasible implies that the "profit" can increase without limit.

False (Graphical solution to a linear programming problem, moderate)

eight. The region that satisfies all of the constraints in graphical linear programming is called the region of optimality.

Imitation (Graphical solution to a linear programming problem, moderate)

9. Solving a linear programming problem with the iso-profit line solution method requires that we move the iso-profit line to each corner of the feasible region until the optimum is identified.

False (Graphical solution to a linear programming problem, moderate)

10. The optimal solution to a linear programming problem is inside the feasible region.

True (Graphical solution to a linear programming problem, moderate)

11. For a linear programming trouble with the constraints 2X + 4Y ≤ 100 and 1X + 8Y ≤ 100, two of its corner points are (0, 0) and (0, 25).

Faux (Graphical solution to a linear programming trouble, moderate) {AACSB: Analytic Skills}

501

12. In linear programming, if there are three constraints, each representing a resources that can be used upward, the optimal solution must employ upwardly all of each of the 3 resources.

False (Graphical solution to a linear programming trouble, moderate)

thirteen. The region that satisfies the constraint 4X + 15Z ≥ grand includes the origin of the graph.

False (Graphical solution to a linear programming problem, easy) {AACSB: Analytic Skills}

14. The optimal solution of a linear programming problem that consists of ii variables and six constraints volition probably not satisfy all half-dozen constraints precisely.

True (Graphical solution to a linear programming problem, difficult)

xv. Sensitivity analysis of linear programming solutions can use trial and error or the analytic postoptimality method.

True (Sensitivity analysis, like shooting fish in a barrel)

16. In sensitivity analysis, a zero shadow price (or dual value) for a resource normally means that the resource has not been used upwardly.

True (Sensitivity analysis, hard)

17. The graphical method of solving linear programming tin can handle only maximizing issues.

Simulated (Solving minimization problems, moderate)

18. In linear programming, statements such as "the alloy must consist of at least 10% of ingredient A, at least thirty% of ingredient B, and no more than 50% of ingredient C" tin be fabricated into valid constraints fifty-fifty though the percentages do not add up to 100 pct.

Truthful (Linear programming applications, difficult) {AACSB: Cogitating Thinking}

MULTIPLE CHOICE

19. Which of the following represents valid constraints in linear programming?

a. 2X ≥ 7X*Y

b. 2X * 7Y ≥ 500

c. 2X + 7Y ≥ 100

d. 2X 2 + 7Y ≥ 50

e. All of the above are valid linear programming constraints.

c (Requirements of a linear programming trouble, moderate)

twenty. Which of the following is not a requirement of a linear programming problem?

a. an objective office, expressed in terms of linear equations

b. constraint equations, expressed as linear equations

c. an objective function, to be maximized or minimized

d. alternative courses of activeness

e. for each decision variable, there must be one constraint or resource limit

e (Requirements of a linear programming problem, moderate)

502

21. In linear programming, a statement such as "maximize contribution" becomes a(n)

a. constraint

b. slack variable

c. objective role

d. violation of linearity

e. decision variable

c (Formulating linear programming problems, moderate)

22. The feasible region in the diagram below is consistent with which i of the following constraints?

a. 8X1 + 4X2 ≤ 160

b. 8X1 + 4X2 ≥ 160

c. 4X1 + 8X2 ≤ 160

d. 8X1 - 4X2 ≤ 160

e. 4X1 - 8X2 ≤ 160

b (Graphical solution to a linear programming problem, difficult) {AACSB: Analytic Skills}

503

23. The viable region in the diagram below is consistent with which one of the following constraints?

a. 8X1 + 4X2 ≥ 160

b. 4X1 + 8X2 ≤ 160

c. 8X1 - 4X2 ≤ 160

d. 8X1 + 4X2 ≤ 160

e. 4X1 - 8X2 ≤ 160

d (Graphical solution to a linear programming problem, moderate) {AACSB: Analytic Skills}

24. An iso-turn a profit line

a. can be used to assistance solve a profit maximizing linear programming trouble

b. is parallel to all other iso-profit lines in the same trouble

c. is a line with the same turn a profit at all points

d. none of the higher up

e. all of the higher up

e (Graphical solution to a linear programming problem, moderate)

25. Which of the following combinations of constraints has no feasible region?

a. X + Y > 15 and X – Y < x

b. Ten + Y > v and X > 10

c. 10 > 10 and Y > 20

d. X + Y > 100 and X + Y < 50

e. All of the above have a feasible region.

d (Graphical solution to a linear programming problem, moderate) {AACSB: Analytic Skills}

504

26. The corner indicate solution method requires

a. finding the value of the objective office at the origin

b. moving the iso-profit line to the highest level that still touches some office of the feasible region

c. moving the iso-turn a profit line to the lowest level that yet touches some function of the feasible region

d. finding the coordinates at each corner of the feasible solution space

e. none of the above

d (Graphical solution to a linear programming problem, moderate)

27. Which of the following sets of constraints results in an unbounded maximizing trouble?

a. X + Y > 100 and X + Y < 50

b. Ten + Y > 15 and X – Y < 10

c. Ten + Y < x and Ten > 5

d. 10 < 10 and Y < 20

due east. All of the above take a bounded maximum.

b (Graphical solution to a linear programming problem, moderate) {AACSB: Analytic Skills}

28. The region which satisfies all of the constraints in graphical linear programming is chosen the

a. expanse of optimal solutions

b. expanse of feasible solutions

c. profit maximization space

d. region of optimality

e. region of non-negativity

b (Graphical solution to a linear programming problem, moderate)

29. Using the graphical solution method to solve a maximization problem requires that we

a. find the value of the objective role at the origin

b. move the iso-profit line to the highest level that still touches some function of the feasible region

c. move the iso-toll line to the lowest level that notwithstanding touches some office of the feasible region

d. apply the method of simultaneous equations to solve for the intersections of constraints

e. none of the to a higher place

b (Graphical solution to a linear programming problem, moderate)

505

xxx. For the two constraints given below, which bespeak is in the viable region of this maximization

problem? (1) 14x + 6y < 42		(two) 10 - y < iii
a.	10 = 2, y = 1
b.	10 = 1, y = 5
c.	x = -ane, y = 1
d.	ten = 4, y = 4
due east.	x = ii, y = viii

a (Graphical solution to a linear programming problem, moderate) {AACSB: Analytic Skills}

31. For the two constraints given beneath, which betoken is in the feasible region of this minimization

problem? (i) 14x + 6y > 42		(two) x - y > 3
a.	10 = -ane, y = ane
b.	x = 0, y = iv
c.	x = 2, y = 1
d.	x = 5, y = 1
east.	10 = ii, y = 0

d (Graphical solution to a linear programming problem, moderate) {AACSB: Analytic Skills}

32. What combination of 10 and y will yield the optimum for this problem? Maximize $3x + $15y, subject to (one) 2x + 4y < 12 and (2) 5x + 2y < x.

a. x = 2, y = 0

b. x = 0, y = three

c. ten = 0, y = 0

d. x = 1, y = 5

e. none of the above

b (Graphical solution to a linear programming problem, moderate) {AACSB: Analytic Skills}

33. What combination of ten and y will yield the optimum for this problem? Minimize $3x + $15y, subject to (ane) 2x + 4y < 12 and (2) 5x + 2y < ten.

a. x = ii, y = 0

b. ten = 0, y = three

c. x = 0, y = 0

d. x = 1, y = 5

e. none of the to a higher place

c (Graphical solution to a linear programming trouble, moderate) {AACSB: Analytic Skills}

34. What combination of a and b will yield the optimum for this trouble? Maximize $6a + $15b, subject to (1) 4a + 2b < 12 and (2) 5a + 2b < 20.

a. a = 0, b = 0

b. a = 3, b = 3

c. a = 0, b = 6

d. a = half dozen, b = 0

eastward. cannot solve without values for a and b

c (Graphical solution to a linear programming trouble, moderate) {AACSB: Analytic Skills}

506

35. A maximizing linear programming problem has two constraints: 2X + 4Y < 100 and

3X + 10Y < 210, in add-on to constraints stating that both 10 and Y must be nonnegative. The corner points of the feasible region of this problem are

a. (0, 0), (50, 0), (0, 21), and (20, xv)

b. (0, 0), (70, 0), (25, 0), and (15, twenty)

c. (20, xv)

d. (0, 0), (0, 100), and (210, 0)

eastward. none of the higher up

a (Graphical solution to a linear programming problem, moderate) {AACSB: Analytic Skills}

36. A linear programming trouble has ii constraints 2X + 4Y ≤ 100 and 1X + 8Y ≤ 100. Which of the post-obit statements about its feasible region is true?

a. There are four corner points including (50, 0) and (0, 12.v).

b. The two corner points are (0, 0) and (l, 12.v).

c. The graphical origin (0, 0) is non in the feasible region.

d. The feasible region includes all points that satisfy one constraint, the other, or both.

eastward. The feasible region cannot be determined without knowing whether the problem is to be minimized or maximized.

a (Graphical solution to a linear programming problem, moderate) {AACSB: Analytic Skills}

37. A linear programming problem has ii constraints 2X + 4Y ≥ 100 and 1X + 8Y ≤ 100. Which of the following statements near its feasible region is true?

a. There are four corner points including (l, 0) and (0, 12.5).

b. The two corner points are (0, 0) and (50, 12.5).

c. The graphical origin (0, 0) is in the viable region.

d. The viable region is triangular in shape, bounded by (l, 0), (33-ane/iii, 8-i/3), and (100, 0).

east. The viable region cannot be determined without knowing whether the trouble is to exist minimized or maximized.

d (Graphical solution to a linear programming problem, moderate) {AACSB: Analytic Skills}

38. A linear programming problem has 2 constraints 2X + 4Y = 100 and 1X + 8Y ≤ 100, plus nonnegativity constraints on X and Y. Which of the following statements near its feasible region is true?

a. The points (100, 0) and (0, 25) both lie outside the feasible region.

b. The 2 corner points are (33-1/3, 8-ane/three) and (50, 0).

c. The graphical origin (0, 0) is not in the feasible region.

d. The feasible region is a directly line segment, not an area.

eastward. All of the above are truthful.

east (Graphical solution to a linear programming problem, moderate) {AACSB: Analytic Skills}

39. A linear programming problem contains a restriction that reads "the quantity of Ten must exist at least three times equally large every bit the quantity of Y." Which of the post-obit inequalities is the proper conception of this constraint?

a. 3X ≥ Y

b. X ≤ 3Y

c. X + Y ≥ 3

d. Ten – 3Y ≥ 0

e. 3X ≤ Y

d (Formulating linear programming problems, moderate) {AACSB: Analytic Skills}

507

twoscore. A linear programming problem contains a brake that reads "the quantity of Q must be no larger than the sum of R, S, and T." Formulate this as a constraint ready for use in problem solving software.

a. Q + R + S + T ≤ 4

b. Q ≥ R + S + T

c. Q – R – S – T ≤ 0

d. Q / (R + S + T) ≤ 0

e. none of the above

c (Formulating linear programming problems, moderate) {AACSB: Analytic Skills}

41. A linear programming problem contains a brake that reads "the quantity of S must be no less than i-fourth as large every bit T and U combined." Formulate this as a constraint ready for apply in trouble solving software.

a. S / (T + U) ≥ four

b. S - .25T -.25U ≥ 0

c. 4S ≤ T + U

d. S ≥ 4T / 4U

due east. none of the above

b (Formulating linear programming problems, moderate) {AACSB: Analytic Skills}

42. A firm makes 2 products, Y and Z. Each unit of Y costs $10 and sells for $forty. Each unit of Z costs $v and sells for $25. If the firm's goal were to maximize sales revenue, the appropriate objective function would exist

a. maximize $40Y = $25Z

b. maximize $40Y + $25Z

c. maximize $30Y + $20Z

d. maximize 0.25Y + 0.20Z

e. none of the above

c (Formulating linear programming bug, moderate) {AACSB: Analytic Skills}

43. A linear programming problem has three constraints: 2X + 10Y ≤ 100

4X + 6Y ≤ 120

6X + 3Y ≤ 90

What is the largest quantity of 10 that tin be made without violating whatsoever of these constraints?

a. fifty

b. xxx

c. xx

d. fifteen

east. ten

d (Graphical solution to a linear programming trouble, moderate) {AACSB: Analytic Skills}

44. In sensitivity assay, a zero shadow price (or dual value) for a resources normally means that

a. the resource is scarce

b. the resource constraint was redundant

c. the resources has not been used up

d. something is incorrect with the trouble formulation

eastward. none of the above

c (Sensitivity analysis, difficult)

508

45. A shadow toll (or dual value) reflects which of the following in a maximization problem?

a. the marginal gain in the objective realized by subtracting i unit of a resource

b. the market price that must exist paid to obtain boosted resource

c. the increase in profit that would accompany ane added unit of a deficient resource

d. the reduction in cost that would accompany a one unit decrease in the resources

e. none of the above

c (Sensitivity analysis, moderate)

46. A linear programming problem has three constraints: 2X + 10Y ≤ 100

4X + 6Y ≤ 120

6X + 3Y ≥ 90

What is the largest quantity of Ten that can exist made without violating whatever of these constraints?

a. 50

b. thirty

c. 20

d. 15

e. 10

b (Graphical solution to a linear programming problem, moderate) {AACSB: Analytic Skills}

47. A maximizing linear programming trouble with variables X and Y and constraints C1, C2, and C3 has been solved. The dual values (not the solution quantities) associated with the problem are

X = 0, Y = 0, C1 = $two, C2 = $0.l, and C3 = $0. Which statement below is false?

a. One more than unit of measurement of the resource in C1 would add $2 to the objective function value.

b. One more unit of the resources in C2 would add together one more unit each of X and Y.

c. The resource in C3 has non been used upward

d. The resources in C1 and in C2, but non in C3, are deficient.

east. All of the to a higher place are true.

b (Sensitivity analysis, difficult) {AACSB: Analytic Skills}

48. A maximizing linear programming problem with variables X and Y and constraints C1, C2, and C3 has been solved. The dual values (non the solution quantities) associated with the problem are

X = 0, Y = $x, C1 = $2, C2 = $0.fifty, and C3 = $0. Which argument below is true?

a. One more than unit of the resource in C1 would reduce the objective office value by $two.

b. Ane more than unit of measurement of the resource in C2 would add together one-half unit of measurement each of X and Y.

c. The resources in C1 and C2 take not been used up.

d. The optimal solution makes only 10; the quantity of Y must be zip.

eastward. All of the above are true.

d (Sensitivity analysis, difficult) {AACSB: Analytic Skills}

509

49. A linear programming maximization problem has been solved. In the optimal solution, two resource are scarce. If an added amount could be establish for only ane of these resources, how would the optimal solution be inverse?

a. The shadow cost of the added resource volition rise.

b. The solution stays the same; the extra resources can't be used without more of the other scarce resource.

c. The extra resource will cause the value of the objective to fall.

d. The optimal mix will be rearranged to employ the added resources, and the value of the objective part volition rise.

e. none of the in a higher place

d (Sensitivity analysis, moderate) {AACSB: Analytic Skills}

Fill-in-THE-Blank

50. ____________ is a mathematical technique designed to aid operations managers plan and brand decisions relative to the trade-offs necessary to allocate resources.

Linear programming (Introduction, like shooting fish in a barrel)

51. The requirements of linear programming bug include an objective function, the presence of constraints, objective and constraints expressed in linear equalities or inequalities, and _________. alternative courses of activeness (Requirements of a linear programming trouble, easy)

52. The _______________ is a mathematical expression in linear programming that maximizes or minimizes some quantity.

objective function (Requirements of a linear programming trouble, piece of cake)

53. ___________ are restrictions that limit the degree to which a managing director can pursue an objective.

Constraints (Requirements of a linear programming problem, moderate)

54. The _____________ is the set of all viable combinations of the conclusion variables. viable region (Graphical solution to a linear programming trouble, moderate)

55. 2 methods of solving linear programming issues past manus include the corner indicate method and the_______________.

iso-profit (or iso-cost) line method (Sensitivity analysis, moderate)

56. _______________ is an analysis that projects how much a solution might change if there were changes in the variables or input data.

Sensitivity analysis (Sensitivity assay, moderate)

57. Two methods of conducting sensitivity analysis on solved linear programming problems are

_______________ and ________________.

postoptimal analytical method, trial and mistake (Sensitivity assay, moderate)

58. A synonym for shadow cost is ______________. dual value (Sensitivity analysis, moderate)

510

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