Determine the projected forecast for the seventh year. Determine the project production for the 2nd and 3rd quarters in the seventh year.

The annual increases in total production are:
Year 2: $250,000 - 200,000 = 50,000$
Year 3: $295,000 - 250,000 = 45,000$
Year 4: $340,000 - 295,000 = 45,000$
Year 5: $390,000 - 340,000 = 50,000$
The pattern of increases is $50,000, 45,000, 45,000, 50,000$. Assuming this pattern continues, the next increase will be 45,000, followed by 50,000.

Projected Year 6 total production: $390,000 + 45,000 = 435,000$
Projected Year 7 total production: $435,000 + 50,000 = 485,000$

i) The projected forecast for the seventh year is $\boxed{\text{485,000}}$.

The increases in Quarter Two production are:
Year 2: $55,000 - 45,000 = 10,000$
Year 3: $70,000 - 55,000 = 15,000$
Year 4: $80,000 - 70,000 = 10,000$
Year 5: $100,000 - 80,000 = 20,000$
The average annual increase for Quarter Two is $\frac{10,000 + 15,000 + 10,000 + 20,000}{4} = \frac{55,000}{4} = 13,750$.

Projected Year 6 Quarter Two production: $100,000 + 13,750 = 113,750$
Projected Year 7 Quarter Two production: $113,750 + 13,750 = 127,500$

The increases in Quarter Three production are:
Year 2: $80,000 - 65,000 = 15,000$
Year 3: $90,000 - 80,000 = 10,000$
Year 4: $100,000 - 90,000 = 10,000$
Year 5: $95,000 - 100,000 = -5,000$
The average annual increase for Quarter Three is $\frac{15,000 + 10,000 + 10,000 - 5,000}{4} = \frac{30,000}{4} = 7,500$.

Projected Year 6 Quarter Three production: $95,000 + 7,500 = 102,500$
Projected Year 7 Quarter Three production: $102,500 + 7,500 = 110,000$

ii) The projected production for the 2nd quarter in the seventh year is $\boxed{\text{127,500}}$.
The projected production for the 3rd quarter in the seventh year is $\boxed{\text{110,000}}$.

Part 4: Define the following appraisal indicators

i) Net Present Value (NPV): The difference between the present value of cash inflows and the present value of cash outflows over a period of time. It is used to evaluate the profitability of a project or investment.

ii) Payback Period: The length of time required for an investment to recover its initial cost from the cash flows it generates. It is a simple measure of an investment's risk and liquidity.

iii) Cash Flow: The total amount of cash or cash equivalents moving into and out of a business. It indicates how well a company manages its cash position, meaning how much cash it generates to pay its debt obligations and fund its operating expenses.