state and prove Theorem Holomorphy of Rλ

                                    A         B          C          D         E

Fixed Startup Cost        $3400 $2200 $2750 $1800 $1200
Cost per MW-hr          $6        $5        $7        $7        $8
Maximum Capacity      2200    1900    2600    1600    3200

Part A: Formulate a Binary-Integer Problem that minimizes the total cost. Write the complete algebraic form, and clearly state the decision variables, objective function, and the constraints.

Hint: Some binary variables and big number constraints are needed in this problem

Part B: Set up and solve a linear spreadsheet model to determine the operating plan that will minimize their overall costs. For full credit, the model must be linear (no multiplication of changing cells, no IF statements, no MAX statements, etc.)

The Ponchatrain Bridge is a​ 16-mile toll bridge that crosses Lake Ponchatrain in New Orleans.​ Currently, there are 7 toll​ booths, each staffed by an employee. Since Hurricane​ Katrina, the Port Authority has been considering replacing the employees with machines. Many factors must be considered because the employees are unionized. ​ However, one of the Port​ Authority's concerns is the effect that replacing the employees with machines will have on the times that drivers spend in the system. Customers arrive to any one toll booth at a rate of 12 per minute. In the exact change lanes with​ employees, the service time is essentially constant at 4 seconds for each driver. With​ machines, the average service time would still be 4 ​seconds, but it would be negative exponential rather than​ constant, because it takes time for the coins to rattle around in the machine.

For the​ "Exact Change​ Lane" with employee

The average time driver spends waiting to pay the toll ​= __ seconds​ (round your response to two decimal​ places).

The average time spent by a driver in the toll system​ (waiting and​ paying) ​= __ seconds​ (round your response to two decimal​ places)

The average number of drivers waiting in the line to pay the toll at a toll

booth​=__ drivers​ (round your response to two decimal​ places).

The average number of drivers at any toll​ booth, namely, in the system ​= __ drivers​ (round your response to two decimal​ places).

For the lane with the proposed machine

The average time driver spends waiting to pay the toll ​= __ seconds​ (round your response to two decimal​ places).

The average time spent by a driver in the toll system​ (waiting and​ paying) ​= __ seconds​ (round your response to two decimal​ places).

The average number of drivers waiting in the line to pay the toll at a toll booth​= __ drivers​ (round your response to two decimal​ places).

The average number of drivers at any toll​ booth, namely, in the system drivers​ __ (round your response to two decimal​ places).

As a result of proposed​ change, the average time spent per driver waiting in the line to pay the toll increases by __ (round your response to the nearest whole​ number).

As a result of proposed​ change, the average time spent per driver in the toll system increases by __ (round your response to the nearest whole​ number).

As a result of proposed​ change, the average number of drivers waiting in the line to pay the toll increases by (round your response to the nearest whole​ number).

As a result of proposed​ change, the average number of drivers at any toll booth increases by​ (round your response to the nearest whole​ number).

t^2 y'' − 4ty' + 6y = t^4*e^t , t > 0. Use variation of parameters to find a particular solution given that y1 = t^2 and y2 = t^3 are a fundamental set of solutions to the corresponding homogeneous equation

On a separate sheet of paper, practice the clustering technique to develop a topic for the writing assignment. Follow the instructions: 1. Choose one of the suggested topics. Write the topic in a large circle in the center. 2. Think about the topic for one or two minutes. Then write each new idea that comes into your mind in smaller circles around the large circle. 3. Think about the idea in each smaller circle for one or two minutes. Write any new ideas in even smaller circles. 4. Look over your groups of circles. Which groups have the largest number of ideas? These are probably the most productive ideas for your paragraph. TOPICS • a word that describes your home culture • an important term from your major field of study • a definition of what a good teacher is • a definition of culture shock • what the word success means to you • a definition of a what a leader is

STEP 3: Write the first draft. • Write FIRST DRAFT at the top of your paper. • Begin your paragraph with a topic sentence. Use the definition from your cluster diagram. As needed, modify the definition so that it is like the ones you wrote in Practice 4 on page 126. . For unity, present your supporting information in a logical order. • Use transition signals to make your paragraph coherent. . Try to include a word origin and/or idiom that goes well with your topic. Pay attention to sentence structure. Include a variety of sentence patterns: simple, compound, and complex sentences. Use adjective clauses and appositives. Punctuate them correctly. • Write a conclusion that tells why the topic is important, interesting, or unique. • Write a title. It should clearly identify your topic. For examples, look at the titles of the models in this chapter

write a definition paragraph on one of the topics:

Soundex produces x Model A radios and y Model B radios. Model A requires 15 min of work on Assembly Line I and 10 min of work on Assembly Line II. Model B requires 10 min of work on Assembly Line I and 12 min of work on Assembly Line II. At most, 25 labor-hours of assembly time on Line I and 22 labor-hours of assembly time on Line II are available each day. It is anticipated that Soundex will realize a profit of $15 on model A and $12 on model B. How many clock radios of each model should be produced each day in order to maximize Soundex's profit?

Prove by induction:

1 + 1/4 + 1/9 +⋯+ 1/?^2 < 2 − 1/?,

for all integers ?>1

The table shows the estimated percentage P of the population of a certain country that are mobile-phone subscribers. (End of year estimates are given.)

(c) Estimate the instantaneous rate of growth in 2003 by sketching a graph of P and measuring the slope of a tangent. (Sketch your graph so that it is a smooth curve through the points, and so that the tangent line has an x-intercept of 1999.3 and passing through the point

(2006, 46.6).  Round your answer to two decimal places.)

For part, c use the two points that are on the tangent line to determine the slope, which is the instantaneous rate of change.
.........................................  percentage points per year

y"+y'-6y=1

1. general solution of corresponding homogenous equation

2. particular solution

3.solution of initial value problem with initial conditions y(0)=y'(0)=0

Express the equation of the plane in explicit form
a. d = [1, -3, -5]; e = [-2, 1, -1] and f = [5, -1, -3] Express the equation of the plane through d, e, and f explicitly
b. d = [-1, 7, -6]; e = [2, -1, 3] and f = [4, -2, 9] Express the equation of the plane through d, e, and f explicitly

Let A =

and eigenvalue λ1 = 3 and associated eigenvector v(1) = (1, 0, 1)t . Find the second dominant eigenvalue λ2 (or the approximation to λ2) by the Wielandt Dflation method

1.

Use Euler's method with step size 0.50.5 to compute the approximate yy-values y1≈y(0.5), y2≈y(1),y3≈y(1.5), and y4≈y(2) of the solution of the initial-value problem

y′=1+3x−2y,   y(0)=2.

y1=

y2=

y3=

y4=

2.  

Consider the differential equation dy/dx=6x, with initial condition y(0)=3

A. Use Euler's method with two steps to estimate y when x=1:

y(1)≈ (Be sure not to round your calculations at each step!)

Now use four steps:
y(1)≈

B. What is the solution to this differential equation (with the given initial condition)?
y=

C. What is the magnitude of the error in the two Euler approximations you found?
Magnitude of error in Euler with 2 steps =

Magnitude of error in Euler with 4 steps =

D. By what factor should the error in these approximations change (that is, the error with two steps should be what number times the error with four)?
factor =

(How close to this is the result you obtained above?)