Physics 341: Problem Set #8 Solutions
1. The vertical motion of stars in spiral galaxies depends on the gravity exerted by the
disk, so it allows us to weigh the disk.
(a) Use dimensional analysis to derive an estimate of the mass density of a spiral
gala
540:453 Production Control
Lecture 16: Aggregate Planning (Ch. 4)
Prof. T. Boucher
1
Aggregate Production Planning Problem
Given
Forecasted aggregate demand covering the selected
planning horizon
The alternative means available to adjust capacity, to w
540:453 Production Control
Lecture 10: Inventory Control and
Uncertain Demand
Prof. T.O. Boucher
1
Effect of Demand on EOQ:
Deterministic vs. Stochastic
Inv
Q=600
Inv
LT=3 wk
Q=600
Reorder
Point=300
LT=3 wk
LT=3 wk
Reorder
Point=300
Time
Place Order
Order
540:453 Production Control
Lecture 8: Sensitivity of EOQ and
Exchange Curves
Prof. T.O. Boucher
1
The basic EOQ model
The EOQ model forms the basis for all the inventory control
models. It treats the basic trade-off between the fixed cost of
ordering and
540:453 Production Control
Lecture 5: Inventory Control s.t. Known
Demand (Ch. 4)
Prof. T. Boucher
1
Topic Areas in Production and
Operations Analysis
Forecasting
Inventory Control: Deterministic Environments
Inventory Control: Stochastic Environments
Agg
540:453 Production Control
Lecture 4: Forecasting (Ch. 2)
Prof. T. Boucher
1
Winters Method: Exponential Smoothing
w/ Trend and Seasonality
Basic Data Pattern
2
Winters Method: Exponential Smoothing
w/ Trend and Seasonality
Data Generating Process
X t ,
540:453 Production Control
Lecture 3: Forecasting (Ch. 2)
Prof. T. Boucher
1
Exponential Smoothing
A type of weighted moving average that applies declining
weights to past data
Weights most recent data more strongly
Reacts more to recent changes
Widel
540:453 Production Control
Lecture 2: Forecasting (Ch. 2)
Prof. T. Boucher
1
Introduction to Forecasting
What is forecasting?
Primary function is to predict the future
Not just a guess
Definite methods of predicting future events
Why are we intereste
Physics 341: Problem Set #11
due November 20
1. Light from the H transition of hydrogen is emitted at a wavelength
Recall that for light, = c.
= 656.28 nm.
(a) Consider a star moving directly away from an observer on Earth at a speed v =
13, 000 km s 1 (l
Physics 341: Problem Set #10
due November 18
You are encouraged to work in groups on these problems, but each student must write up
the solutions individually. You must also list your collaborators on your solutions, and cite
any external sources you used
Physics 341: Problem Set #10 solutions
1. In this problem you will calculate a microlensing light curve. In the gure below, the
dashed straight line represents the trajectory of a point source passing behind a point
mass lens (the solid dot in the center)
Physics 341: Problem Set #9
due November 11
1. The Plummer model for a spherical star cluster is given by the density prole
(r) =
3M
a2
4 (r2 + a2 )5/2
where M is the total mass, and a is a core radius.
(a) Show that the enclosed mass in the Plummer model
Physics 341: Problem Set #9 Solutions
1. The Plummer model for a spherical star cluster is given by the density prole
(r) =
3M
a2
4 (r2 + a2 )5/2
where M is the total mass, and a is a core radius.
(a) Show that the enclosed mass in the Plummer model is
M
Physics 341: Problem Set #7
due October 28
You are encouraged to work in groups on these problems, but each student must write up
the solutions individually. You must also list your collaborators on your solutions, and cite
any external sources you used (
Physics 341: Problem Set #7 Solutions
1. Recall that the surface brightness of an exponential disk has the form
I (R) = I0 e
R/hR
where I0 is the central surface brightness and hR is the disk scale length. The total
brightness is given by integrating this
Physics 341: Problem Set #6
due October 16
You will need to make some assumptions to answer some of these questions. Explain your
reasoning, and show your work!
1. You may have heard that a person falling feet-rst into a black hole would be stretched
out
Phys 341: Homework #5 Solutions
1. (a) If the Earth and Moon are tidally locked and the Earths rotation period is 47 days, the
the Moons orbital period is also P = 47 days = 4.1 106 s. Then from Keplers Third
Law, the semimajor axis of the Moons orbit is