The following time series shows the sales of a particular product over the past 12 months.

1. The following time series shows the sales of a particular product over the past 12 months.

Month Sales
1105
2135
3 120
4 105
5 90
6 120
7 145
8140
9 100
10 80
11 100
12 110

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a. Construct a time series plot. What type of pattern exists in the data?
b. use a 5 0.3 to compute the exponential smoothing values for the time series.
c. u se trial and error to find a value of the exponential smoothing coefficient a that results in a relatively small MSE.

2. AutoIgnite produces electronic ignition systems for automobiles at a plant in Cleveland, Ohio. Each ignition system is assembled from two components produced at AutoIgnite’s plants in Buffalo, New York, and Dayton, Ohio. The Buffalo plant can produce 2000 units of component 1, 1000 units of component 2, or any combination of the two components each day. For instance, 60% of Buffalo’s production time could be used to produce component 1 and 40% of Buffalo’s production time could be used to produce component 2; in this case, the Buffalo plant would be able to produce 0.6(2000) = 1200 units of component 1 each day and 0.4(1000) = 400 units of component 2 each day. The Dayton plant can produce 600 units of component 1, 1400 units of component 2, or any combination of the two components each day. At the end of each day, the component production at Buffalo and Dayton is sent to Cleveland for assembly of the ignition systems on the following workday.

a. Formulate a linear programming model that can be used to develop a daily production schedule for the Buffalo and Dayton plants that will maximize daily production of ignition systems at Cleveland.
b. Find the optimal solution.