Judith Thompson runs a florist shop on the Gulf Coast of Texas, specializing in
ID: 3177446 • Letter: J
Question
Judith Thompson runs a florist shop on the Gulf Coast of Texas, specializing in floral arrangements for weddings and other special events. She advertises weekly in the local newspapers and is considering increasing her advertising budget. Before doing so, she decides to evaluate the past effectiveness of those ads. Five weeks are sampled, and the advertising dollars and sales volume for each of these is shown in following table:
Sales($1,000)
(Y)
Advertising ($100) (X)
11
5
6
3
10
7
6
2
12
8
Develop a regression equation that would help Judith to evaluate her advertisement.
Forecast the Sale when .
Find the coefficient of determination for the model obtained in above Question 1.
From historical data, Harry’s Car Wash estimates that dirty cars arrive at the rate of 10 per hour all day Saturday. With a crew working the wash line, Harry figures that cars can be cleaned at the rate of one every 5 minutes. One car at a time is cleaned in this example of a single-channel waiting line.
Assuming Poisson arrivals and exponential service times, find the
Utilization rate of the car wash.
Average time a car waits before it is washed.
Average time a car spends in the service system.
The students patiently form a single line in front of the desk to wait for help at University. Student arrivals are best described by Poisson distribution with mean of 15 students per hour arriving at the help desk. The help desk server can help an average one student in 3 minutes, with the service rate being described by an exponential distribution. Calculate the following characteristics of the service system:
The average number of students in the system.
The average number of students waiting in the line.
Probability that no student is in the system.
The Electro comp Corporation manufactures two electrical products: air conditioners and large fans. The assembly process for each is similar in that both require a certain amount of wiring and drilling. Each air conditioner takes 3 hours of wiring and 2 hours of drilling. Each fan must go through 2 hours of wiring and 1 hour of drilling. During the next production period, 240 hours of wiring time are available and up to 140 hours of drilling time may be used. Each air conditioner sold yields a profit of $25. Each fan assembled may be sold for a $15 profit. Formulate this LP production mix situation.
Solve the LPP formulated above in Question 5 using corner point Graphical approach to find the best combination of air conditioners and fans that yields the highest profit.
Sales($1,000)
(Y)
Advertising ($100) (X)
11
5
6
3
10
7
6
2
12
8
Explanation / Answer
For the Judith Thomson data, the model is built in R:
> tt <- read.csv("clipboard",sep=" ")
> tt
Y X
1 11 5
2 6 3
3 10 7
4 6 2
5 12 8
> xylm <- lm(Y~X,tt)
> summary(xylm)
Call:
lm(formula = Y ~ X, data = tt)
Residuals:
1 2 3 4 5
2.00e+00 -1.00e+00 -1.00e+00 -2.22e-16 2.22e-16
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.0000 1.5242 2.624 0.0787 .
X 1.0000 0.2774 3.606 0.0366 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 1.414 on 3 degrees of freedom
Multiple R-squared: 0.8125, Adjusted R-squared: 0.75
F-statistic: 13 on 1 and 3 DF, p-value: 0.03662
The coefficient of determination is this 81.25%.
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