[Q1: A firm's demand function is given as P = 24 -3X where P = price and X quantity produced and sold . Determine.

I. The output for maximum revenue and show it is a maximum.(3marks)

2. What is the price at maximum revenue. (2marks)

Q2. The cost account of a firm producing personal computers has worked out the total cost function for the firm as TC = 120Q + Q2+0.02Q3.A sales manager has provided the sales forecasting function as P = 114 - 0.025Q where P is price and Q the quantity sold.

1. Find the level of production that will yield minimum average cost per unit and determine whether this level of output maximizes profit for the firm.(4marks).

2. Determine the. Price that will maximize profit for the firm.(4marks)

3. Determine the maximum revenue for this firm.(3marks)

Q3. A police department believes that the number of serious crimes which occur each month can be estimated by the equation C = 1200 - 12p where C equals the number of serious crimes expected per month and P equals the number of officers assigned to preventive patrol. If c is graphed on the vertical axis .

1. Identify the slope and interpret its meaning (2marks).

2. Identify the C intercept andinterpret its meaning (2marks).

3. Identify the intercept and interpret its meaning. (2marks).

Q4. The cost account of a firm producing personal computers has worked out the total cost function for the firm as TC = 120Q + Q2+0.02Q3.A sales manager has provided the sales forecasting function as P = 114 - 0.025Q where P is price and Q the quantity sold.

1. Find the level of production that will yield minimum average cost per unit and dete

rmine whether this level of output maximizes profit for the firm.(4marks).

2. Determine the. Price that will maximize profit for the firm.(4marks)

3. Determine the maximum revenue for this firm.(3marks)

[Q[7 A police department believes that the number of serious crimes which occur each month can be estimated by the equation C = 1200 - 12p where C equals the number of serious crimes expected per month and P equals the number of officers assigned to preventive patrol. If c is graphed on the vertical axis .

1. Identify the slope and interpret its meaning (2marks).

2. Identify the C intercept andinterpret its meaning (2marks).

3. Identify the intercept and interpret its meaning. (2marks).