The trend of annual sales of BALCO is described by the eq Y= 12+ 0.7x ...
Conversion of Annual Sales to Monthly Sales
Given equation: Y= 12 0.7x (Origin: 1970, X unit 1 year, Y unit annual production)
Step 1: Half the Origin
Since we need to convert annual sales to monthly sales, we need to halve the origin. Therefore, the new origin becomes 1st January 1970 instead of 1970.
Step 2: Conversion Formula
We know that there are 12 months in a year. Therefore, we need to divide the annual sales by 12 to get the monthly sales. The conversion formula is:
Monthly sales = Annual sales / 12
Step 3: Conversion of Equation
Now, we can use the conversion formula to convert the given equation to a monthly basis:
Y(monthly) = Y(annual) / 12
Substituting Y(annual) with the given equation:
Y(monthly) = (12 0.7x) / 12
Simplifying the equation:
Y(monthly) = 0.9976 + 0.0049x
Explanation of the Equation
The converted equation shows that the monthly sales of BALCO are a function of time (x). The constant term 0.9976 represents the initial monthly sales of BALCO, which is almost equal to the annual sales (12) divided by 12. The coefficient of x, 0.0049, represents the increase in monthly sales per unit of time (1 month).
Therefore, the equation can be used to predict the monthly sales of BALCO based on the time period. For example, if x equals 12, which represents December 1970, the predicted monthly sales would be:
Y(monthly) = 0.9976 + 0.0049(12) = 1.0594
This means that BALCO is predicted to sell 1.0594 units in December 1970.