42. Which of the graph/s above contains an Euler Trail? A. A and D...

42. Which of the graph/s above contains an Euler Trail?

A. A and D

B. B and C

C. A, B, and C

D. B, C, and D

43. Which of the graph/s above is/are Eulerian?

A. None of the graphs

B. Only B

C. Only C

D. B and C

44. Which of the graph/s above is/are Hamiltonian?

A. A and B

B. A and C

C. A, B, and D

D. A, C, and D

45. What is the minimum distance between points C and F?

A. 9

B. 10

C. 11

D. 12

46. Which of the following is a Hamiltonian Circuit for the given graph?

A. AIBGCDEFHA

B. DICBAIHGFED

C. FIBAHGCDEF

D. GFEIDCBAHG

47. What is the length of the Hamiltonian Circuit described in number 46?

A. 35

B. 37

C. 39

D. 41

48. Which vertex in the given graph has the highest degree?

A. Vertex C

B. Vertex F

C. Vertex H

D. Vertex I

49. Which is referred to as an edge connecting the same vertex?

A. Circuit

B. Loop

C. Path

D. Repeated Edge

50. Which of the following statements is/are true?

i. The vertices of K4 all have degrees equal to 3.

ii. K4 is eulerian.

iii. K4 is Hamiltonian.

A. I and II

B. II and III

C. I and III

D. I, II, and III

II. PROBLEM SOLVING (20 POINTS). Show complete neat and organized solution. (define the

variables, LP model, feasible region, optimal solution, final answer in statement form)

Mike must work at least 18 hours a week to supplement his income while attending school.

He has the opportunity to work in two retail stores. In store 1, he can work between

5 and 13 hours a week, and in store 2, he is allowed between 6 and 11 hours. Both stores pay

the same hourly wage. In deciding how many hours to work in each store, Mike wants to

base his decision on work stress. Based on interviews with present employees, Mike estimates

that, on an ascending scale of 1 to 10, the stress factors are 8 and 6 at stores 1 and 2,

respectively. Because stress mounts by the hour, he assumes that the total stress for each

store at the end of the week is proportional to the number of hours he works in the store. How

many hours should Mike work in each store?