I NEED A LIST OF ALL OF THE CONSTRAINTS

Case 1 Description - Planning an Advertising Campaign

The Flamingo Grill is an upscale restaurant located in St. Petersburg, Florida. To help plan an advertising campaign for the coming season, Flamingo's management team hired the advertising firm of Haskell & Johnson (HJ). The management team requested HJ's recommendation concerning how the advertising budget should be distributed across television, radio, and newspaper advertisements. The budget has been set at $279,000.

In a meeting with Flamingo's management team, HJ consultants provided the following information about the industry exposure effectiveness rating per ad, their estimate of the number of potential new customers reached per ad, and the cost for each ad.

The exposure rating is viewed as a measure of the value of the ad to both existing customers and potential new customers. It is a function of such things as image, message recall, visual and audio appeal, and so on. As expected, the more expensive television advertisement has the highest exposure effectiveness rating along with the greatest potential for reaching new customers.

At this point, the HJ consultants pointed out that the data concerning exposure and reach were only applicable to the first few ads in each medium. For television, HJ stated that the exposure rating of 90 and the 4000 new customers reached per ad were reliable for the first 10 television ads. After 10 ads, the benefit is expected to decline. For planning purposes, HJ recommended reducing the exposure rating to 55 and the estimate of the potential new customers reached to 1500 for any television ads beyond 10. For radio ads, the preceding data are reliable up to a maximum of 15 ads. Beyond 15 ads, the exposure rating declines to 20 and the number of new customers reached declines to 1200 per ad. Similarly, for newspaper ads, the preceding data are reliable up to a maximum of 20; the exposure rating declines to 5 and the potential number of new customers reached declines to 800 for additional ads.

Flamingo's management team accepted maximizing the total exposure rating, across all media, as the objective of the advertising campaign. Because of management's concern with attracting new customers, management stated that the advertising campaign must reach at least 100,000 new customers. To balance the advertising campaign and make use of all advertising media, Flamingo's management team also adopted the following guidelines. Use at least twice as many radio advertisements as television advertisements.

• Use no more than 20 television advertisements
• The television budget should be at least $140,000
• The radio advertising budget is restricted to a maximum of $99,000
• The newspaper budget is to be at least $30,000

HJ agreed to work with these guidelines and provide a recommendation as to how the $279,000 advertising budget should be allocated among television, radio, and newspaper advertising.

Now, prepare a managerial report developing a model that can be used to determine the advertising budget allocation for the Flamingo Grill. Include a discussion of the following in your report,

1. A schedule showing the recommended number of television, radio, and newspaper advertisements and the budget allocation for each medium. Show the total exposure and indicate the total number of potential new customers reached.

2. How would the total exposure change if an additional $10,000 were added to the advertising budget?

3. A discussion of the ranges for the objective function coefficients. What do the ranges indicate about how sensitive the recommended solution is to HJ's exposure rating coefficients?

4. Independent of Q2, suppose a new marketing research data shows that for radio advertisements beyond 15 ads, the exposure rating declines to 15 (instead of 20 described earlier), and while for newspaper advertisement beyond 20 the exposure rating declines to 7 (instead of 5 described earlier). What would be the campaign plan then, and the resulted total exposure?

5. Independent of Q2-4, suppose that the Flamingo’s management team has raised the TV and newspaper minimum budgets to $150,000 and $40,000 respectively. What would be the campaign plan then, the resulted total exposure and new customers reached?

6. Independent of Q2-5, after reviewing HJ's recommendation in Q1, the Flamingo's management team asked how the recommendation would change if the objective of the advertising campaign was to maximize the number of potential new customers reached. Develop the media schedule under this objective.

7. Compare the recommendations made from Q1 and Q6. What is your final recommendation for the Flamingo Grill's advertising campaign?

Managerial Report – General Format

A managerial report should be prepared and should be easily understood by the general recipients of the report (supervisors, COO, CEO, clients, etc.)

The report should include:

1. An executive summary (a short description of the case, alternatives considered, recommendations based on different objectives and a final recommendation)
2. A short description of key assumptions used in the model / analysis
3. Linear programming model defining all decision variables
4. Printouts of the optimal solution obtained by using Excel. Include printouts from various alternatives/objectives considered
5. Narrative discussion explaining the LP model, alternatives considered, brief analysis on what if questions Q4 and Q5, what detailed analysis you made to come up with the recommendations in Q1 and Q6 and how you compared them to arrive at a final recommendation in Q7.

I NEED A LIST OF ALL OF THE CONSTRAINTS!

Q−3: [5×4 marks]
a. Find a, b if a+2b=107 mod 9 and 2a+b=-55 mod 7.
b. Write the prime factorization of 229320 and 49140, hence find GCD and LCM.
c. Convert the following number (1303)4 to base 5.
d. Using the Prime Factorization technique determine whether 173 is a prime.
e. Use the cipher: f(x)=(x+7) mod 26 to decrypt “THAO ALZA”.

Question 1:

a) What are the complex roots of x^8-1 ?

b) What are the irreducible factors of f(x)=x^8-1 in R[x]?

c) What are the irreducible factors of f(x)=x^8-1 in Q[x]?

1. Show that the set of all polynomials of deg=2 is not a vector space over reals.

can this be fixed, can we have a set of polynomials that is a vector space over reals?

2. Show that the set of 2x2 matrices with m_22 = 1 is not a vector space over reals.

3. Show that the set of infinitely-differentiable real functions is a a vector space under pointwise function addition, and pointwise scalar multiplication as defined in class, is a vector space over reals.

4. Show that the set of infinitely differentiable real functions such that f(0)=2, is not a vector space over reals.

please answer 1-4 thankyou

A programmer is writing the code for a new interactive basketball game. As a result, she is using quadratic relations to model the path of the ball. During the game, when a ball is shot, the path it follows is modelled by the quadratic relation, h= -0.2d^2 + 3d +6, where h represented the height of the ball above the ground and d represented the distance of the ball from the shooter. Both distances are measured in feet.

1. How high was the ball when the shooter shot it?
2. What was the maximum height obtained by the ball?
3. A rim of a basketball net is 10 feet high. For what distance was the ball above the rim of the basketball net?
4. How far would the shooter have to be away from the rim of the basketball net for the ball to hit the rim of the basketball net and possibly go in?
5. Create a graphical model, using technology, to verify your calculations.
6. Create your own quadratic relation that would model the path of a shot from a distance of 15 feet that would hit the rim of the basketball net. Explain how you obtained your answer.

Provide step-by-step solutions that are communicated clearly for all questions.

A tank is filled to capacity with 400 gallons water containing 30 lbs of salt. Brine containing 2 lbs of salt per gallon is pumped into the tank at a rate of 3 gallons per minute. The well mixed solution is pumped out at rate of 3.5 gallons per minute. Determine the differential equation of the model and solve for an equation relating amount of salt in tank at time t. Determine the time until the tank is empty.

managing a work order backlog is not the most exciting of maintenance task but without a complete and up-to date backlog. important work will be forgotten indeed, good backlog management is a perequisite for effective planning and scheduling. discuss an optimum size for non-shutdown work order backlog for a typical 24/7 continuous -process operation and includes if a backlog too small and if the backlog too large

The unequally spaced data given in Table 2 were generated from f(x)=3xcos(x)

Table 2

a) Calculate f^''(0.1), f^''(0.95) and f^'' (0.3) by using the appropriate divided difference
(forward, backward and central) equations which will give the most accurate result.
Compute the true percent relative error for each case.

b) Evaluate the integral from a=0.1 to b=0.95 using a combination of the trapezoidal and
Simpson’s rules; employ Simpson’s rule wherever possible to obtain the highest
accuracy. Compute the true percent relative error.

The XYZ Data Corporation has assigned three perspective new apprentices to collect data on the corporation’s current computer processing demands to determine which apprentice should be hired. The corporation knows that its data usage is modeled by a linear function, since each new client added has approximately the same computer processing requirement. Your supervisor at XYZ has assigned you the task of reviewing the data collected by the three apprentices to determine which apprentice collected the data accurately. Additionally, you are to use the correct data to forecast at what client level the model will reach XYZ’s current maximum computing capacity of 50 terabytes.

Explain mathematically, how you determined the correct data set, and why each of the other data sets are not linear. Be sure to convert the relevant information into various mathematical forms (e.g., equations, graphs, diagrams, tables, words) to model the linear data. In other words, be sure to show how you would “visually” convince your supervisor at the XYZ Data Corporation which apprentice had accurately collected the date. Discuss the differences in the rates of change for each data set and how this can be utilized to determine linear data. Discuss how you made judgments and drew appropriate conclusions based on the analysis of observable facts, while at the same time recognizing the limits of this analysis. Be sure to note important assumptions you made in the estimation, modeling, and data analysis.

Your response should identify the calculations needed, explain how you organized the appropriate data, and show the performed calculations, so your discussion is compelling and memorable (precisely stated, appropriately visualized, and logical conclusions strongly supported). Be sure to use grammatically correct sentence structure, and your narrative should clearly exhibit the relationship between your visual communications and your narrative conclusions.

FRANK’S DATA

x                           0                            1                            2                            3                          4                               5

y = f(x)                 10                         11.5                      13.25                    15.2                      17.5                               20.2

GABBY’S DATA

x                           0                           1                            2                            3                            4                               5

y = g(x)                 10                         11.15                    12.3                      13.45                    14.6                               15.75

HYATT’S DATA

x                           0                            1                            2                           3                            4                               5

y = h(x)                10                         14.0                      17.9                     19.9                      21.5                               22.9

Montreal Manufacturing Inc. has the following cost and production data for the month of April.

The beginning inventory was 60% complete for conversion costs. The ending inventory was 40% complete for conversion costs. Materials are added at the beginning of the process.

Costs pertaining to the month of April are as follows:

Show that the set of complex numbers ℂ= {x+iy|x and y are real, i²=-1} is a vector space. Verify each of the 10 axioms.

5.52. Potency of a drug. Eli Lilly and Company has developed three methods (G, R1, and R2) for esti- mating the shelf life of its drug products based on potency. One way to compare the three methods is to build a regression model for the dependent variable, estimated shelf life y (as a percentage of true shelf life), with potency of the drug (x1) as a quantitative predictor and method as a qualitative predictor.

(a) Write a first-order, main effects model for E(y) as a function of potency (x1) and method. SAS Output for Exercise 5.51

(b) Interpret the β coefficients of the model, part a.

(c) Write a first-order model for E(y) that will allow the slopes to differ for the three methods.

(d) Refer to part c. For each method, write the slope of the y – x1 line in terms of the β’s.

brief history on Camassa-Holm equation for fun!

find an alternative 
definition of the degree of a vertex of a graph. 
please be detailed as possible thank you