Quantitative Methods Test 2 (Ch. 6-8)

In a basic assignment problem where we have 4 teams of officials and 4 game locations, all supply and demand values equal:

1

A PERT/CPM activity has an optimistic time estimate of 3 days, a most likely time estimate of 8 days, and a pessimistic time estimate of 10 days. The standard deviation (in days) of this activity is:

1.16

What is the expected project completion time?

12

(Figure 2) Consider the network diagram given in Figure 2. Assume that the amount on each branch is the distance in miles between the respective nodes. What is the distance for the shortest route from the source node (Node 1) to Node 5?

13

What is the minimum number of miles of cable to be used to connect all six nodes?

18 miles

Determine the slack for Activity D.

2

Activity Predecessor Time A - 10 B A 8 C A 9 D B 13 E B 8 F B, D 9 G C, E, F 6 What is the fastest time to complete this project?

46

Consider the network diagram given in the figure. how many constraints are required to model this as a linear program?

6

A PERT/CPM activity has an optimistic time estimate of 3 days, a most likely time estimate of 8 days, and a pessimistic time estimate of 10 days. The expected time (in days) of this activity is:

7.5

Consider the network diagram given in the figure. How many decision variables are in this problem?

8

Consider the following network, which shows the location of various facilities within a youth camp and the distances (in tens of yards) between each facility. Walking trails will be constructed to connect all the facilities. In order to preserve the natural beauty of the camp (and to minimize the construction time and cost), the directors want to determine which paths should be constructed. Use this network to determine which paths should be built. Select all arcs that are part of the final solution.

AC; AE; BG; DE; EF; EG

The assignment problem constraint x31 + x32 + x33 + x34 <= 2 means:

Agent 3 can be assigned to no more than 2 tasks

In a balanced transportation model where supply equals demand:

All constraints are equalities

In a transportation problem, items are allocated from sources to destinations:

At a minimum cost

The LS and LF are calculated using the:

Backward pass through the network that is moving from right to left

If an activity cannot be delayed without affecting the entire project, then it is a _____ activity.

Critical

If t is the expected completion time for a given activity, then:

EF = ES + t

The critical path is the _____ path through the network.

Longest

The activities that must be completed prior to the start of an activity in question are called the immediate _____ of the activity in question.

Predecessors

In the linear programming formulation of a transportation network:

The sum of variables corresponding to arcs out of a source node is constrained by the supply at that node; there is one variable for each arc; there is one constraint for each node (All of the above)

The general problem that deals with the distribution of goods from a source to a destination, like shipping a truckload of oranges from Los Angeles to St. Louis, is the:

Transportation problem

Consider the following network representation of shipment routes between plants, a distribution center, and retail outlets. The numbers next to the arcs represent shipping costs. For example, the cost of shipping from plant 1 to distribution center 3 is equal to $2. Assume that Plant 1 can supply 500 units and Plant 2, 500 units. Demand at the retail outlets are: Outlet 4, 300 units; Outlet 5, 250 units; Outlet 6, 450 units. Which constraint represents transshipment through the distribution center?

x13 + x23 - x34 - x35 - x36 >= 0

Which constraint represents the quantity shipped to retail outlet 6 if exactly 450 units are required?

x36 + x26 = 450

The linear programming model for a transportation problem has constraints for supply at each _____ and _____ at each destination.

Source; demand

The local Internet provider wants to develop a network that will connect its server at its satellite center in Valparaiso with the main city computer centers in Northwest Indiana to improve the Internet service and to minimize the amount of cable used to connect network nodes. If we represent this problem with a network:

The length of cables in miles are the branches, and the cities are the nodes