Answers based on engineering management

$\sum Y = 200,000 + 250,000 + 295,000 + 340,000 + 390,000 = 1,475,000$
$\sum XY = 1(200,000) + 2(250,000) + 3(295,000) + 4(340,000) + 5(390,000)$
$\sum XY = 200,000 + 500,000 + 885,000 + 1,360,000 + 1,950,000 = 4,895,000$

The regression equation is $Y = 47,000X + 154,000$.

The projected forecast for the seventh year is $\boxed{\text{483,000 units}}$.

2.a (ii) Determine the project production for the 2nd and 3rd quarters in the seventh year.

$\sum Y_{Q2} = 45,000 + 55,000 + 70,000 + 80,000 + 100,000 = 350,000$
$\sum XY_{Q2} = 1(45,000) + 2(55,000) + 3(70,000) + 4(80,000) + 5(100,000)$
$\sum XY_{Q2} = 45,000 + 110,000 + 210,000 + 320,000 + 500,000 = 1,185,000$

The regression equation for Q2 is $Y_{Q2} = 13,500X + 29,500$.

The projected production for the 2nd quarter in the seventh year is $\boxed{\text{124,000 units}}$.

$\sum Y_{Q3} = 65,000 + 80,000 + 90,000 + 100,000 + 95,000 = 430,000$
$\sum XY_{Q3} = 1(65,000) + 2(80,000) + 3(90,000) + 4(100,000) + 5(95,000)$
$\sum XY_{Q3} = 65,000 + 160,000 + 270,000 + 400,000 + 475,000 = 1,370,000$

The regression equation for Q3 is $Y_{Q3} = 8,000X + 62,000$.

The projected production for the 3rd quarter in the seventh year is $\boxed{\text{118,000 units}}$.

2.b) Define the following appraisal indicators:

• i) Net Present Value (NPV) The Net Present Value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows over a period of time. It is a capital budgeting technique used to assess the profitability of a project or investment. A positive NPV indicates that the project is expected to generate more value than its cost, making it a potentially desirable investment.

• ii) Payback Period (PBP) The Payback Period (PBP) is the amount of time required for an investment to generate enough cash inflows to recover its initial cost. It is a simple method to evaluate the risk and liquidity of a project, with shorter payback periods generally preferred as they imply faster recovery of capital and lower risk exposure.

• iii) Cash Flow (CF) Cash Flow refers to the net amount of cash and cash equivalents moving into and out of a business or project. It represents the actual movement of money, distinguishing it from accounting profit. Cash flow is vital for assessing a company's liquidity and solvency, and it is typically categorized into operating, investing, and financing activities.