You have been given data that represents quarterly sales in ($000's) of a Rad's Pizza delivery service for the first four years of their operation. The company wants to use the partial Excel Summary Output and the Time Series data below to develop a regression equationand use seasonal indexes to estimate their sales. Note: time periods (t=1, 2, 3, ...)

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	67.4	2.470180883	27.28545	1.5413E-13	62.10198893	72.6980111
t	0.299	0.255460025	1.168595	0.262081145	-0.24937785	0.84643667

	Quarter	Sales (Y)	t		Y/y hat
Year 1	Q1	65			0.960
	Q2	70			1.029
	Q3	66			0.966
	Q4	76			1.108
Year 2	Q1	65			0.943
	Q2	69			0.997
	Q3	67			0.964
	Q4	78			1.118
Year 3	Q1	67			0.956
	Q2	69			0.980
	Q3	68			0.962
	Q4	77			1.085
Year 4	Q1	66
	Q2	68
	Q3	69
	Q4	79

Required:

1. Calculate theseasonal indexesto three decimal places, show your calculations. (6 marks)
2. Forecast the sales for quarter 3 of year 5. (2 marks)

Question # 4 (7 marks)A manufacturing company makes two brands of a product (A and B). Each unit of brand A requires 2 hours of machine time for processing and 2 hours for finishing. Each unit of brand B requires 4 labor hours of machine time for processing and 2 hours for finishing. The maximum number of machine hours for processing and finishing are 180 and 100 respectively. The company has already secured orders of 30 units of brand A. In addition, the company makes a profit of $3.52 on each unit of brand A and $4.20 on each unit of brand B.Required:

1. State the objective function and the constraints related to the above conditions. 3 marks
2. Sketch the constraints to this linear programming problem, determine the points that make the feasible regionand theoptimal number of A and B. (show your calculations). 4 marks