Spring is right around the corner and that can mean only one thing: it’s time to incubate
some eggs for a fresh crop of chickens to supplement the existing flock for the year.
There are three breeds that are popular: Leghorns, Buff Orpingtons, and Cochins, and
each has its own strengths and weaknesses. The Leghorns, for example, are superb
layers but easily excitable. The Cochins, on the other hand, are very even-tempered but
not the best layers. They do have marvelous plumage, with feathers that extend down to
their feet. The Buff Orpingtons are good layers, have interesting plumage, and are
mid-range in their temperament.
The chicken farmer would like this crop of chickens to produce as many eggs as
possible while keeping the noise to a dull roar and having a nice array of birds
free-ranging on his lawn during those lazy summer days. He has put the relevant data in
table form. Plumage numbers are on a scale from 1-10, with 10 being the most
desirable. The egg output is not on a scale, but is instead the average output for the
breed, based on years of collecting eggs.
Temperament is actually measured by the average volume of cackling, clucking, and
crowing and is measured in decibels per bird. Appetite is measured in ounces of layer
pellets per week consumed by each of the breeds, while fertilizer is measured as the
output in ounces per week.
What is a full set of constraints if the farmer wants this flock to produce less than 100
decibels of noise and more than 5 pounds of fertilizer, consume less than 10 pounds of
layer pellets, and achieve a total plumage score of at least 75?
The ________ for a mixed strategy game assumes that the game is played many times.
The reduced cost (shadow price) for a positive decision variable is ________.
________ is the difference between the payoff from the best decision and all other
decision payoffs.
In certain applications, the transition matrix may first need to be divided into
submatrices. The identity matrix, I, and matrix Q (the nonabsorbing matrix) are then
used to determine the ________ matrix.
An investor has $80,000 to invest in three stocks, stock A costs $100, stock B costs
$120 and stock C costs $80. Each stock A has a risk factor of 8, each stock B has a risk
factor of 10 and each stock C has a risk factor of 7. The investor believes that the sum
of the risk factors for all stocks purchase should not exceed 6000. The projected annual
growth rate for the three stocks are 9%, 13% and 8% respectively. The projected annual
dividend income from these stocks are as follows: Stock A: $14/stock, Stock B:
$15/stock, and Stock C: $20/stock. The investor desires an annual dividend income of
$10,000. The investor has established the following goals in order of their importance:
(1) The investor believes that the budget cannot be exceeded. (d1)(2) The risk factor
should not exceed the target amount of 6000. (d2)(3) The average annual growth rate in
stock prices must be at least 10%. (d3)(4) The investor desires a dividend income of at
least $10,000. (d4)
Write the risk factor constraint
A(n) ________ problem can be identified in the simplex procedure when it is not
possible to select a pivot row.
We begin the branch and bound method by first solving the problem as a regular
________ model without integer restrictions.
Sara has found an unlimited source of catnip so that is no longer a constraint. However,
customer demand dictates that she produce 2.5 times more catnip balls than mice. Write
the new constraint.
Poultry Processing processes chickens for fast food restaurants. The Majestic chickens
arrive from the farms on trucks, in cages, at a rate of 8 trucks per hour according to the
Poisson distribution. The quality standards of Poultry Processing require that the
chickens be processed within 30 minutes, which includes the time from when the trucks
arrive until the chickens are finished processing. Determine the maximum average
processing rate (in truckloads per hour) that must be designed for the machine, in order
to ensure that the cages will be processed, on the average, in 30 minutes or less. Assume
processing time is exponentially distributed.
Refer to the table below to answer the question(s) that follow:
If the early start for activity A is equal to 23 months and the duration of activity A is
equal to 5 months, what is the earliest finish for activity A?
The Wiethoff Company has a contract to produce 10,000 garden hoses for a customer.
Wiethoff has four Different machines that can produce this kind of hose. Because these
machines are from Different manufacturers and use Differing technologies, their
specifications are not the same.
Write the objective function.
Given the following linear programming problem:
maximize Z = $100x1 + 80x2
subject to x1 + 2x2 ≤ 40
3x1 + x2 ≤ 60
x1, x2 ≥ 0
Using the simplex method, what is the value for S1 in the final basic feasible solution?
The linear programming problem whose output follows determines how many red nail
polishes, blue nail polishes, green nail polishes, and pink nail polishes a beauty salon
should stock. The objective function measures profit; it is assumed that every piece
stocked will be sold. Constraint 1 measures display space in units, constraint 2
measures time to set up the display in minutes. Constraints 3 and 4 are marketing
restrictions.
MAX 100x1 + 120x2 + 150x3 + 125x4
Subject to 1. x1 + 2x2 + 2x3 + 2x4 ≤ 108
2. 3x1 + 5x2 + x4 ≤ 120
3. x1 + x3 ≤ 25
4. x2 + x3 + x4 > 50
x1, x2, x3,x4 ≤ 0
Optimal Solution:
Objective Function Value = 7475.000
Objective Coefficient Ranges
Right Hand Side Ranges
By how much can the amount of space decrease before there is a change in the profit?
The linear programming problem whose output follows determines how many red nail
polishes, blue nail polishes, green nail polishes, and pink nail polishes a beauty salon
should stock. The objective function measures profit; it is assumed that every piece
stocked will be sold. Constraint 1 measures display space in units, constraint 2
measures time to set up the display in minutes. Constraints 3 and 4 are marketing
restrictions.
MAX 100x1 + 120x2 + 150x3 + 125x4
Subject to 1. x1 + 2x2 + 2x3 + 2x4 ≤ 108
2. 3x1 + 5x2 + x4 ≤ 120
3. x1 + x3 ≤ 25
4. x2 + x3 + x4 > 50
x1, x2, x3,x4 ≤ 0
Optimal Solution:
Objective Function Value = 7475.000
Objective Coefficient Ranges
Right Hand Side Ranges
How much time will be used?
Employees of a local company are classified according to gender and job type. The
following table summarizes the number of people in each job category.
Male (M) Female (F)Job
Administrative (AD) 110 10
Salaried staff (SS) 30 50
Hourly staff (HS) 60 40
If an employee is selected at random, what is the probability that the employee is male
and salaried staff?
________ probabilities are average constant probabilities that the system will be in a
state in the future.
Consider the following annual sales data for 2001-2008:
Use the linear regression method and determine the estimated sales equation.
In the expected ________ method, a plan of strategies is determined by each player so
that expected gain of one equals the expected loss of the other.