Compute the manual and solver solution for part A and Part B

The operations manager at a manufacturing facility is about to begin an energy efficiency initiative. As this program begins, it will be helpful to have a benchmark data on energy use, to determine whether the initiative is having an effect. The facilities department has provided data on the monthly energy use (in kilowatt hours) over the past three years, as shown in the table.

1. Use holt winters additive method to estimate the monthly usage for the upcoming 12 months. Use the smoothing parameters alpha=0.3, Beta=0.4 and gamma=0.5
   1. Perform manual analysis using the formulae for holt winters additive method.
   2. Perform analysis with solver.
2. Use holt winters multiplicative method to estimate the monthly usage for the upcoming 12 months. Use the smoothing parameters alpha=0.3, Beta=0.4 and gamma=0.5
   3. Perform manual analysis using the formulae for holt winters multiplicative method.
   4. Perform analysis with solver.

Hint: Since monthly time series data is given in this problem 1 cycle = 1 year and number of time periods in a cycle (p) = 12 since a year comprises of 12 months.

t	Observed
1	31040
2	28720
3	20540
4	22260
5	11550
6	13100
7	14790
8	12360
9	12890
10	9790
11	14840
12	14610
13	24540
14	26560
15	22060
16	16220
17	12920
18	9740
19	10160
20	12740
21	9240
22	11220
23	13780
24	19040
25	32410
26	21380
27	20370
28	18300
29	10020
30	11420
31	10020
32	11800
33	13120
34	10410
35	13510
36	17340