There are a total of four problems from 6 and Ch. 7. Submit three of them as indicated. (If you submit all 4, I will just grade the 3.) You may do all problems in the given Excel template or do Ch. 6 in the Excel template and Ch. 7 in Word.
To Submit: Ch6: D, Ch7: A, B
Ch. 6 Times Series with Trend & Seasonality
In the two problems here, you may use either Excel’s Data Analysis tool (available only in Windows) or LINEST function to find the regression coefficients. All work must be shown.
Hudson Marine has been an authorized dealer for C&D marine radios for the past six years. The number of radios sold each quarter is shown in the Excel template. Hudson Marine would like to forecast the quarterly sales for year 7.
(a) Construct a time series plot.
(b) Construct a multiple regression model with dummy variables to develop an equation that takes into account both trend and seasonality. Give the quarterly forecasts for year 7.
(c) Out of four quarters of the year, which quarter has the peak demand? Which quarter has the lowest demand?
Ch. 7 Linear Programming Formulation
The Outdoor Furniture Corporation manufactures two products, benches and picnic tables. The firm has two main resources: its carpenters (labor force) and a supply of redwood for use in the furniture. During the next production cycle, 1,200 hours of labor are available under a union agreement. The firm also has a stock of 3,500 feet of good-quality redwood.
Each bench that Outdoor Furniture produces requires 6 labor hours and 12 feet of redwood; each picnic table takes 9 labor hours and 40 feet of redwood.
Completed benches will yield a profit of $10 each, and tables will result in a profit of $20 each.
(a) Let B = number of benches to produce and
T = number of tables to produce.
Write down the linear programming model to decide how many benches and tables should be produced to obtain the largest possible profit. Don’t attempt to solve the problem.
(b) Is B = 70, T = 70 feasible solution? How about B= 70, T = 60?
(c) Given an example of a feasible solution that yields total profit of at least $2,000. (There are many such solutions, just give one.) Decimal numbers are OK. The person(s) who gets the highest profit will get 1 extra point on this homework.
Alpine Attic is the charity sponsored by local churches in Denver, Colorado. Literally thousands of items, including televisions and stereos, are donated each year, most in need of repair. Repaired televisions and stereos typically sell for $50 and $30 each at the Alpine Attic Thrift Store. To repair these, Alpine Attic depends on John Lucas who owns JL Electronics, a deacon at St. Paul’s Episcopal Church. Each month, he can donate 45 hours of an electrician’s time and 30 hours of a technician’s time. But this is not enough time to repair all of the televisions and radios donated.
To repair a television, it takes average of 90 minutes of electrician’s time and 30 minutes of a technician’s time.
To repair a stereo, it takes an average of 45 minutes of an electrician’s time and 60 minutes of a technician’s time.
Alpine Attic would like to determine how to best use the electrician’s and technician’s time to realize the maximum possible profit from the donated televisions and stereos. Write down a linear programming model to decide how many televisions and stereos should be repaired each month. Do not attempt to solve. Don’t forget to define the decision variables first.
Data & Computation
Year Quarter Sales (units)
1 1 12
2 1 16
3 1 21
4 1 24
5 1 26
6 1 30
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