Formula required for milk production regime

Question

Month
Herd Size
New Additions in Herd
Milk Production/cow
(Litres)
Total Milk Production
(litres)
Jan
10
10
100
Feb
20
10
10 + 10
100+100
April
20
0
8 + 10
80+100
May
20
0
5 + 10
50+100
June
20
0
2 + 10
20+100
July
40
20
1+8+10
10+80+200
Hello,
I want to make cash flow for dairy farm, as you may know as the time passes the milk production of the cows gradually decreases. As you can see in the table above I have selected the text colour for every new purchase of cow come in the farm. Till now I have manually put the milk produced per cow for every new herd can somebody please help me to make a formula so I do not have to manually decrease the milk production. I just put the new herd size and total milk production automatically calculated in the last column for the next 5 months. thanks
Further Explanation of the table:
First purchase of 10 cows give 10 litres/cow milk for 2 months then they decrease it to 5 litre/cow in the third month. Every new addition in the herd will follow the same pattern.
Apple Numbers 3.5.2.

Answer 1

Hello
You may use SUMPRODUCT() to calculate the total litres for each month such that -
∑ { [number of cows of i'th month] * [liters per cow of i'th month] } : i = 1..N
E.g., (N = 6)
Litres
A1  month
A2  6
A3  5
A4  4
A5  3
A6  2
A7  1
B1  litre/cow
B2  1
B3  2
B4  5
B5  8
B6  10
B7  10
Table 1
A1  month
A2  *
A3  *
A4  *
A5  *
A6  *
A7  Jan
A8  Feb
A9  Mar
A10 Apr
A11 May
A12 Jun
B1  herd size
B2  0
B3  0
B4  0
B5  0
B6  0
B7  =B6+C7
B8  =B7+C8
B9  =B8+C9
B10 =B9+C10
B11 =B10+C11
B12 =B11+C12
C1  new cows
C2  0
C3  0
C4  0
C5  0
C6  0
C7  10
C8  10
C9  0
C10 0
C11 0
C12 20
D1  total litres
D2 
D3 
D4 
D5 
D6 
D7  =SUMPRODUCT(C2:C7,Litres::B$2:B$7)
D8  =SUMPRODUCT(C3:C8,Litres::B$2:B$7)
D9  =SUMPRODUCT(C4:C9,Litres::B$2:B$7)
D10 =SUMPRODUCT(C5:C10,Litres::B$2:B$7)
D11 =SUMPRODUCT(C6:C11,Litres::B$2:B$7)
D12 =SUMPRODUCT(C7:C12,Litres::B$2:B$7)
E1  litres/cow
E2 
E3 
E4 
E5 
E6 
E7  =D7/B7
E8  =D8/B8
E9  =D9/B9
E10 =D10/B10
E11 =D11/B11
E12 =D12/B12
Rows 2 thru 6 in Table 1 are required to keep SUMPRODUCT() from throwing error in rows 7 thru 11.
* Tables are built in Numbers v2.
Hope this may help you get the basic idea.
H