Maurices Pump Manufacturing Company

Provide written linear model and excel formulation using solver for each question:

5-17

Maurice’s Pump Manufacturing Company Currently maintains plants in Atlanta and Tulsa that supply major distribution centers in Los Angeles and New York. Because of an expanding demand, Maurice has decided to open a third plant and has narrowed the choice to one to the two cities- New Orleans or Houston. The pertinent information is listed in excel file under tab 5-17. Note that the costs and capacity listed for New Orleans and Houston are proposed/ anticipated.

5-22

A supply chain consists of three plants (A,B, and C) three distributors, (J,K, and L) and three stores (X,Y, and Z). The relevant supply, demand, and unti shipping cost information are given in the attached excel sheet under tab 5-22. Set up and solve the transshipment model to minimize total shipping costs.

5-25

Cindy Jefferson, hospital administrator at Anderson Hospital must appoint head nurses to four newly established departments: urology, cardiology, orthopedics, and pediatrics. Believing in the decision model in tab 5-25 in the excel sheet, Cindy has interviewed four nurses, Morris, Richards, Cook and Morgan and developed an index scale ranging from 0 to 100 to be used in the assignment. An index of 0 implies the nurse would be a perfect fit to the task. A value close to 100 on the other hand implies that the nurse is not suited to head that unit.  Which nurse should be assigned to each unit.

MATH106 4010 Quiz 2

Directions:
- Read and sign the academic honesty certification statement below, then read the questions
carefully and answer them to the best of your ability. You may write your answers on this sheet
or on the sheet you do your work on, but PLEASE show your work! Follow directions as
outlined in Unit Quiz 2 folder under the Assignments link on our LEO classroom NavBar.
- Test & work is due as specified in Course Schedule. I cannot accept any late submissions!
This is open-book and notes; calculators & graphing devices are authorized for use. Good luck!

I certify the work submitted on and with this document represents my own personal work. I have
not collaborated with, or consulted with, anyone else to produce the work I am submitting. I
certify I have not used any instructor solutions manuals, or any online problem solving services.
I understand and agree to abide by UMUC Policy on Academic Dishonesty and Plagiarism.
_______________________________________
Student Signature & Date
1. For the equation which is graphed below:

a. Determine the slope m:

m = _____________
b. Determine the x intercept:

_____________
c. Determine the y intercept:

_____________
d. State the equation algebraically in slope intercept form:

_____________________________
1

2. 3. Solve for the variable. Check your answer in the original equation, if you determine the
equation has a single solution. For full credit, please show all work, including check step!
2.

5 + 2(9 + 3) = 3( + 5)

____________________
3.

3
5
2
4 = ( + 4) 
2
3
3

____________________

4. Solve the linear inequality. Write your solution set in interval notation and graph it on a
number line. If you are typing the exam, you can easily create a number line and graph
inequalities using your keyboard. How-to link is in Content > Table of Contents > Course
Resources > Webliography in our LEO classroom.
2 < 3x 5 7

Answer : ___________________________
-4 -3 -2 -1 0 1 2 3 4 5
2

5. Christina is selling an antique dining room furniture set through a broker. She wants to get
$2000 for herself, but the broker gets 15% of the selling price as commission. What should the
selling price be?

Answer: ____________________________
6. Multiple Choice: Find the equation of the line passing through (4, 1) and (3, 1):
a. 2x + 5y = 3

c. 5x 4y = 11

b. 3x + 4y = 8

d. 2x + y = 7

Answer: __________________

7. Solve the system of equations using substitution or elimination by addition (your choice).
You MUST show all your work to get credit for this problem!
2 = 5
3 + 5 = 27

Answer: x = ___________ y = _____________
3

8. An outdoor goods store sells a wool shirt costing $20 wholesale for $33 retail, and a coldweather jacket costing $100 for $153. Assume the stores markup policy is linear.
a. Multiple Choice: The equation for retail price P in terms of wholesale cost C is:
.

= 2 7

. = 2 + 3

. =

3
2

7

.

3

=2 +3

Answer: ___________________
b. Multiple Choice: What is the wholesale cost of a tent this store retails for $213 ?
. $147

. $140

. $110

. $105

Answer: __________________

9. As chief financial officer at Amalgamated Pharmaceutical, you track costs and revenue for
the daily manufacturing process for your companys top-selling product, Shovitall, the drug
that relieves math anxiety. Daily production costs $6,300 plus $45 for every case produced.
Daily revenue coming in equates to $115 per case sold.
a. Determine the cost (C) and revenue (R) equations for this manufacturing process

Cost equation:

___________________________________

Revenue equation:

___________________________________

b. How many cases must be sold each day for this manufacturing process to break even?
Your answer must be supported either algebraically or graphically dont just give an answer!

Number of cases sold daily to break even: _________________________
4

10. The following table lists the amount of money Americans spent on antipsychotic drugs
annually from 2004 to 2011 [Source: IMS Institute for Healthcare Informatics, "Use of
Medicines in the United States: Review of 2011"]

Years After 2004 (X - value)

MATH 221 Week 6 iLab

MATH 221 Statistics for Decision Making

Week 6 iLab

Name:_______________________

Statistical Concepts:

• Data Simulation
• Confidence Intervals
• Normal Probabilities

Short Answer Writing Assignment

All answers should be complete sentences.

We need to find the confidence interval for the SLEEP variable.  To do this, we need to find the mean and then find the maximum error.  Then we can use a calculator to find the interval, (x – E, x + E).

First, find the mean.  Under that column, in cell E37, type =AVERAGE(E2:E36).  Under that in cell E38, type =STDEV(E2:E36).   Now we can find the maximum error of the confidence interval.  To find the maximum error, we use the “confidence” formula.  In cell E39, type=CONFIDENCE.NORM(0.05,E38,35).  The 0.05 is based on the confidence level of 95%, the E38 is the standard deviation, and 35 is the number in our sample.  You then need to calculate the confidence interval by using a calculator to subtract the maximum error from the mean (x-E) and add it to the mean (x+E).

1. 1.     Give and interpret the 95% confidence interval for the hours of sleep a student gets.  (5 points)

Then, you can go down to cell E40 and type =CONFIDENCE.NORM(0.01,E38,35) to find the maximum error for a 99% confidence interval.  Again, you would need to use a calculator to subtract this and add this to the mean to find the actual confidence interval.

1. 2.     Give and interpret the 99% confidence interval for the hours of sleep a student gets.  (5 points)

1. 3.     Compare the 95% and 99% confidence intervals for the hours of sleep a student gets. Explain the difference between these intervals and why this difference occurs. (5 points)

In the week 2 lab, you found the mean and the standard deviation for the HEIGHT variable for both males and females.  Use those values for follow these directions to calculate the numbers again.

(From week 2 lab: Calculate descriptive statistics for the variable Height by Gender.  Click on Insert and then Pivot Table.  Click in the top box and select all the data (including labels) from Height through Gender.  Also click on “new worksheet” and then OK.  On the right of the new sheet, click on Height andGender, making sure that Gender is in the Rows box and Height is in the Values box.   Click on the down arrow next to Height in the Values box and selectValue Field Settings.  In the pop up box, click Average then OK.  Write these down.  Then click on the down arrow next to Height in the Values box again and select Value Field Settings.  In the pop up box, click on StdDev then OK.  Write these values down.)

You will also need the number of males and the number of females in the dataset.  You can either use the same pivot table created above by selecting Countin the Value Field Settings, or you can actually count in the dataset.

Then in Excel (somewhere on the data file or in a blank worksheet), calculate the maximum error for the females and the maximum error for the males.  To find the maximum error for the females, type =CONFIDENCE.T(0.05,stdev,#), using the females’ height standard deviation for “stdev” in the formula and the number of females in your sample for the “#”.  Then you can use a calculator to add and subtract this maximum error from the average female height for the 95% confidence interval.  Do this again with 0.01 as the alpha in the beginning of the formula to find the 99% confidence interval.

Find these same two intervals for the male data by using the same formula, but using the males’ standard deviation for “stdev” and the number of males in your sample for the “#”.

1. 4.      Give and interpret the 95% confidence intervals for males and females on the HEIGHT variable.  Which is wider and why?  (7 points)

Math 141 Quiz 7 Problems

1. Determine whether or not the alternating series converge or diverge.
(a)
( 1) n 1

n ln n 1
1

(b)


( 1) n

n
1

2n 2 n 2
5n 2 2n 1

2. Determine whether the series converges absolutely, or converges conditionally, or
diverges and give reasons for your conclusions.
(a)
( 1) n

n 3n 4
1

(b)



( 0.2) n

n
1

3. Use Ratio Test or Root Test to determine whether the following infinite series are
absolutely convergent.
(a)

2n
( 1) n 1 2

n
n
1

(b)
2 
ln n 

n 
2


n

4. Calculate the Maclaurin series for

1
f ( x) 
2x

to the

term.
x3

5. Find the interval of convergence for the power series
(a)

1

x n 1
n 2n 1
1

(b)

n n
x
n
n 2
1




6. Use substitution method and a known power series to find power series for
. Please express your answer in sigma notation.
f ( x) x cos(3 x )

Math 128A Programming Project 01

For the following two problems, write and debug MATLAB codes and make sure they run
with the test autograder from the course web page. Test them thoroughly on test cases
of your own design including simple roots, multiple roots with sign change, and closely
separated roots. When you are convinced they work, submit your codes together with
• brief discussion of any design decisions
• brief comparison of test results with theory
Part 1 Implement a MATLAB function findbracket.m of the form
function [a, b] = findbracket(f, x0)
% f: function handle f(x) to find a zero for
% x0: starting point / center of interval containing a zero
to try to find an initial interval [a, b] containing the input x0 and bracketing a zero of f (x),
i.e. with sgn f (a) = sgn f (b).
Your function should begin with a = b = x0 and a step size δ = 2−k chosen so that
fl (x0 − δ) < fl x0 −

δ
2

= x0

(i.e. the unit of least precision for x0 ). While sgn f (a) = sgn f (b), decrease a by δ, increase
b by δ, evaluate f (a) and f (b). and double δ.
Part 2 Implement a MATLAB function schroderbisection.m of the form
function [r, h] = schroderbisection(a, b, f, fp, fpp, t)
% a: Beginning of interval [a, b]
% b: End of interval [a, b]
% f: function handle f(x) to find a zero for
% fp: function handle f’(x)
% fpp: function handle f’’(x)
% t: User-provided tolerance for interval width
which combines the fast convergence of the Schr¨der iteration for multiple roots
o
g(x) = x −

1
f (x)
f (x)f
f (x) 1 −

(x)
f (x)2

=x−

f (x)f (x)
f (x)2 − f (x)f (x)

with the bracketing guarantee of bisection. At each step j = 1 to n, carefully choose p as in
geometric mean bisection (watch out for zeroes!). Define
= min(|f (b) − f (a)|/8, |f (p)||b − a|2 )
Apply the Schr¨der iteration function g(x) to two equations f± (x) = f (x) ± = 0, yielding
o
two candidates x = q± = g± (p). Replace [a, b] by the smallest interval with endpoints
1

Math 128A, Spring 2016

Programming Project 01

chosen from a, p, q+ , q− and b which keeps the root bracketed. Repeat until a f value exactly
vanishes, b − a ≤ t, or b and a are adjacent floating point numbers, whichever comes first.
Return the final approximation to the root r = (a + b)/2 and a 6 × n history matrix
h[1:6,1:n] with column h[1:6,j] = (a, p, q− , q+ , b, f (p)) recorded at step j.

Code Submission: Upload the MATLAB files findbracket.m and schroderbisection.m
and any supporting files to bCourses for your GSI to grade.