Could someone eplain the highlighted part of this problem Yo

Could someone eplain the highlighted part of this problem?

You have reached the end of the first year of selling Product Y. Below are the monthly sales figures, by unit, from the year (20X1).

By Month (20X1)

Number of units (Product X)

January

1,020

February

1,075

March

1,150

April

1,300

May

1,600

June

2,000

July

2,800

August

4,000

September

5,500

October

7,200

November

10,000

December

15,000

Total

52,645

Current cost structure for Product Y is as follows:
Direct Material - $7 per unit
Direct Labor - $20 per hour (it takes 1 hour to build one unit)
Overhead - $1500 per 5000 units produced

Activity:
Plot the current units of Product Y for 20X1 on a graph. Determine the appropriate mathematical model to forecast future trend, based on the growth rate and expectations, in monthly unit sales expected. Explain your forecast. Draw a timeline for production of Product Y by applying a forecast for Manufacturing Requirements Planning (MRP). Determine the total cost of goods manufactured in 20X1 and calculate the variance from your budget (forecast x cost of the 3 elements of manufacturing) – what is the different between your budgeted cost of goods manufactured and the actual cost of goods manufactured (use the new costs for Product Y).

Solution :

The appropriate mathematical model to forecast future trend is Regression analysis

The linear equation is given by

Y = b₀ + b₁ t

b₁ = 12 X 494920 - 78 X 52645 / 12 X 650 - 78²

b₁ = 1832730 / 1716

b₁ = 1068.02

b₀ = Y_mean - b₁ X_mean

b₀ = 4387.08 - 1068.02 X 6.5

b₀ = -2555.04

Y_t = b₀ + b₁ t

Y_t = -2555.04 + 1068.02 X t

The total cost of goods manufactured in 20X1 = 52645 X $ 7 + 52645 X $ 20 + 15793.50

The total cost of goods manufactured in 20X1 = $ 1,437 , 208.50

Could someone explain how the below values were calculated - thanks :))

The forecasted values are shown below : -

Solution