Question

North Dakota Electric Company estimates its demand trend line (in millions of kilowatt hours) to be:

D= 77 +0.43Q
where Q refers to the sequential quarter number and Q=1 for winter of year 1. In addition, the multiplicative seasonal factors are as follows:
Quarter Factor (index)
winter .8
spring 1.1
summer 1.4
fall .7
Find the forecast of for the four quarters of year of 17.

Answer 1

The demand forecast for the four quarters of the year of 17 is

Demand for winter of year 17 = 83.96 million kWh

Demand for spring of year 17 = 115.92 million kWh

Demand for summer of year 17 = 148.13 million kWh

Demand for fall of year 17 = 74.37 million kWh

Step-by-step explanation:

The North Dakota Electric Company estimates its demand trend line by the following equation.

`D = 77 + 0.43Q`

Where Q is the sequential quarter number.

The multiplicative seasonal factors are as follows:

winter = 0.8

spring = 1.1

summer = 1.4

fall = 0.7

We are asked to find the forecast for the four quarters of the year of 17.

Since the quarter numbers are sequential,

Q = 1 + 16×4

Q = 65 for winter of year 17

Q = 66 for spring of year 17

Q = 67 for summer of year 17

Q = 68 for fall of year 17

Demand Winter year 17:

`D = 77 + 0.43(65) = 104.95 * 0.8 = 83.96`

Demand Spring year 17:

`D = 77 + 0.43(66) = 105.38 * 1.1 = 115.92`

Demand Summer year 17:

`D = 77 + 0.43(67) = 105.81 * 1.4 = 148.13`

Demand Fall year 17:

`D = 77 + 0.43(68) = 106.24 * 0.7 = 74.37`

Therefore, the demand forecast for the four quarters of the year of 17 is

Demand for winter of year 17 = 83.96 million kWh

Demand for spring of year 17 = 115.92 million kWh

Demand for summer of year 17 = 148.13 million kWh

Demand for fall of year 17 = 74.37 million kWh