final practice questions
Which of the following is an equation or an inequality that expresses a resource restriction in a mathematical model? a) a constraint b) a parameter c) an objective function d) a decision variable
a) a constraint
Assume that we are using 0-1 integer programming model to solve a capital budgeting problem and xj = 1 if project j is selected and xj = 0, otherwise. The constraint (x1 + x2 + x3 + x4 = 2) means that ________ out of the ________ projects must be selected. a) exactly 2, 4 b) exactly 1, 2 c) at most 1, 2 d) at least 2, 4
a) exactly 2, 4
A PERT/CPM activity has an optimistic time estimate of 4 days, a most likely time estimate of 6 days, and a pessimistic time estimate of 10 days. The expected time (in days) of this activity is: a) 6.0. b) 6.33. c) 7.0. d) 7.5
b) 6.33.
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 of this activity is: a) 1/3. b) 7/6. c) 7/9. d) 2/3.
b) 7/6.
Which of these statements regarding project crashing is true? a) Crashing is not possible unless there are multiple critical paths. b) Crashing shortens the project duration by assigning more resources to one or more of the critical tasks. c) Activities not on the critical path cannot become critical after crashing. d) Crashing a project often reduces the time it takes for lengthy or complex, but noncritical activities.
b) Crashing shortens the project duration by assigning more resources to one or more of the critical tasks.
Let: rj = regular production quantity for period j, oj =overtime production quantity in period j, ij = inventory quantity in period j, and dj = demand quantity in period j. Correct formulation of the demand constraint for a multiperiod scheduling problem is: a) rj - oj - i1 + i2 ≥ dj. b) rj + oj + i2 - i1 ≥ dj c) rj + oj + i1 - i2 ≥ dj. d) rj + oj + i1 - i2 ≤ dj.
b) rj + oj + i2 - i1 ≥ dj
The minimal spanning tree problem determines the: a) shortest distance between a source node and a destination node. b) maximum amount that can be transported along any one path. c) minimum total branch lengths connecting all nodes in the network d) minimum amount that should be transported along any one path.
c) minimum total branch lengths connecting all nodes in the network
At the break-even point: a) revenue is maximized. b) costs are minimized. c) total revenue equals total cost. d) profit is maximized.
c) total revenue equals total cost.
For a linear programming problem, assume that a given resource has not been fully used. We can conclude that the shadow price associated with that constraint: a) will have a positive value. b) could have a positive, negative or a value of zero. (no sign restrictions). c) will have a value of zero. d) will have a negative value.
c) will have a value of zero.
Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8000 gallons of component 1 available, and the demand gasoline types 1 and 2 are 11,000 and 14,000 gallons, respectively. Write the constraint stating that the component 1 cannot account for more than 35% of the gasoline type 1. a) x11+ x12(.35)(x11 + x21) b) x11+ .35(x11 + x12) c) -.65x11 + .35x21 ≤ 0 d) .65x11 -.35x21 ≤ 0
d) .65x11 -.35x21 ≤ 0
It costs $50,000 to start a production process. Variable cost is $25 per unit and revenue is $45 per unit. What is the break-even point? a) 2000 units b) 1111 units c) 1000 units d) 2500 units
d) 2500 units
The first step of the maximal flow solution method is to: a) add the maximal flow along the path to the flow in the opposite direction at each node. b) select the node with the shortest direct route from the origin. c) select any starting node. d) arbitrarily select any path in the network from origin to destination.
d) arbitrarily select any path in the network from origin to destination.
The term ________ refers to testing how a problem solution reacts to changes in one or more of the model parameters. a) decision analysis b) graphical solution c) break-even analysis d) sensitivity analysis
d) sensitivity analysis
In a mixed integer model, the solution values of the decision variables must be 0 or 1. true false
false
In a transportation problem, a demand constraint (the amount of product demanded at a given destination) is a less-than-or equal-to constraint (≤). true false
false
Multiple optimal solutions occur only when constraints are parallel to each other. true false
false
The optimal solution for a graphical linear programming problem is always the corner point that is the farthest from the origin. true false
false
The sensitivity range for an objective function coefficient is the range of values over which the profit does not change. true false
false