Cambrian Railways runs a daily container freight train between Cardiff and Birmingham. Its major customer Welsh Farming Co-operative has a demand for containers by the equation:

P = 410-5Q, where P is the unit selling price and Q is quantity of units in thousands.

Cambrian's total cost function is given by the equation:

TC = 3Q² + 10Q 100, where TC is total costs in thousands of dollars.

Required:

1. Determine the output level at which profit is maximized. (7 marks)

2. Compute the optimal price per unit that maximizes profit. (3 marks)

3. Determine the optimal sales revenue that would maximize profit (3 marks)

4. Calculate the maximum profit. (5 Marks)

5. Identify two factors to consider when in arriving at pricing decisions within the organization. (2 marks)