Question

The following equation summarizes the trend portion of quarterly sales of condominiums over a long cycle. Sales also exhibit seasonal variations.

F_t = 52 − 4.2t + 3.2t ²
  
where
F_t = Unit sales
t = 0 at the first quarter of last year

Quarter	Relative
1	1.00
2	1.00
3	.50
4	1.50

Using the information given, prepare a forecast of sales for each quarter of next year (not this year), and the first quarter of the year following that. (Round intermediate calculations and final answers to 2 decimal places.)

Quarter	Forecast
1
2
3
4
1

Answer 1

Quarter	Forecast
1	223.2
2	273.4
3	165
4	589.5
1	462.4

Quarter	I	2	3	4	5
t	8	9	10	11	12
Ft	223.2	273.4	330	393	462.4
Relative	1.00	1.00	.50	1.50	1.00
Forecast	223.2	273.4	165	589.5	462.4

Ft at t = 8

= 52 − 4.2t + 3.2t 2

= 52 - 4.2 * 8 + 3.2 *8 ^ 2

= 223.2

Ft at t = 9

= 52 − 4.2t + 3.2t 2

= 52 - 4.2 * 9 + 3.2 *9^2

= 273.4

Ft at t = 10

= 52 − 4.2t + 3.2t 2

= 52 - 4.2 * 10 + 3.2 * 10^2

= 330

Ft at t = 11

= 52 − 4.2t + 3.2t 2

= 52 - 4.2 * 11 + 3.2 * 11 ^ 2

= 393

Ft at t = 12

= 52 − 4.2t + 3.2t 2

= 52 - 4.2 * 12 + 3.2 * 12^2

= 462.4