The Lagrange multiplier, λ, reflects a change in the objective function from a unit
change in the ________ value of a constraint.
The ________ normal distribution has a mean of 0 and a standard deviation of 1.
Write the Lagrangian function for the following nonlinear program:
Min x1
2 + 2x2
2 – 8x1 – 12x2 + 34
subject to: x1
2 + 2x2
2 = 5
L = x1
Lenny, a graduate research assistant “moonlights” at the short order counter in the
student union snack bar in the evenings. He is the only one on duty at the counter
during the hours he works. Arrivals to the counter seem to follow the Poisson
distribution with a mean of 8 per hour. Each customer is served one at a time and the
service time follows an exponential distribution with a mean of 5 minutes.
What is the likelihood that there are three or fewer customers in the entire system? How
does this compare with the likelihood of three or fewer customers in a system with the
same arrival and service rates but staffed by four servers?
The number of cars arriving at Joe Kelly’s oil change and tune-up place during the last
200 hours of operation is observed to be the following:
Determine the probability distribution of car arrivals.
Refer to the table below to answer the question(s) that follow:
What is the estimated standard deviation (in weeks) for the critical path completion
time?
Assume price and demand are related by the following function: v = 100 – 2.5p. If fixed
cost = $5000 and variable cost = $10, then the expression for profit is ________.
The ________ connects all nodes in a network so that the total branch lengths are
minimized.
A plant has four jobs to be assigned to four machines, and each machine has
XOAXOAerent manufacturing times for each product. The production manager wants
to determine the optimal assignments of four jobs to four machines to minimize total
manufacturing time. This problem can be most efficiently solved using the ________
model.
In a ________ inventory system, a constant amount is ordered when inventory declines
to a predetermined level.
A large book publisher has five manuscripts that must be edited as soon as possible.
Five editors are available for doing the work; however, their working times on the
various manuscripts will XOAXOAer based on their backgrounds and interests. The
publisher wants to use an assignment method to determine who does which manuscript.
Estimates of editing times (in hours) for each manuscript by each editor are:
How many constraints are needed?
Given the following linear programming problem:
maximize 4x1 + 3x2
subject to 4x1 + 3x2 ≤23
5x1 – x2 ≤ 5
x1, x2 ≥ 0
What is the (Ci– Zi) value for S2 at the initial solution?
In a network flow problem, ________ represent junction points connecting branches.
William ran the original model in Excel and discovered that he was walking away from
significant income. He reformulated the model with a new profit constraint of 16R +
24W + d2
+ + d2
– = 550.
All of the other constraints and priorities remained the same. Based on this snippet of
the answer report, what happens during this production run?
The local grocery store consists of two cashiers. The customers arrive at the checkout
according to the Poisson distribution and the service times are based on negative
exponential distribution. The average customer service time is 4 minutes and the
average time between the arrivals of successive customers is 3 minutes. Assume that
customers equally divide themselves between the two cashiers.
On average, how many customers are waiting in line to be served?
In solving a minimization problem, artificial variables are assigned a ________ in the
objective function to eliminate them from the final solution.
An appropriate choice of a model for analyzing the best shipping routes for a supply
chain consisting of a manufacturer, warehouse, and retailer would be the ________
model.