1. Given a firm’s demand function, P = 24 - 0.5Q and the average cost function, AC = Q2 – 8Q + 36 + 3/Q,
calculate the level of output Q which
a) maximizes total revenue b) maximizes profits
. Given a firm’s demand function, P = 24 - 0.5Q and the average cost function, AC = Q2 – 8Q + 36 + 3/Q,
calculate the level of output Q which
a) maximizes total revenue b) maximizes profits
. Given a firm’s demand function, P = 24 - 0.5Q and the average cost function, AC = Q2 – 8Q + 36 + 3/Q, calculate the level of output Q which a) maximizes total revenue b) maximizes profits
4. Discuss how resistance to change could be managed in an organization. Briefly describe with reference to an organization how change was managed successfully. Briefly describe the organization you are referring to.
5. Briefly describe the competencies required for a change agent and discuss the diverse roles of a change agent.
5. A sample of 48 tools produced by a machine shows the following sequence of good (G) and defective (D) tools:
G G G G G G D D G G G G G G G G
G G D D D D G G G G G G D G G G
G G G G G G D D G G G G G D G G
Test the randomness at the 0.05 significance level.
2. Given a firm’s demand function, P = 24 - 0.5Q and the average cost function, AC = Q2 – 8Q + 36 + 3/Q, calculate the level of output Q
1. Given a firm’s demand function, P = 24 - 0.5Q and the average cost function, AC = Q2 – 8Q + 36 + 3/Q, calculate the level of output Q which a) maximizes total revenue
b) maximizes profits
. Given a firm’s demand function, P = 24 - 0.5Q and the average cost function, AC = Q2 – 8Q + 36 + 3/Q, calculate the level of output Q which a) maximizes total revenue
b) maximizes profits
To solve this problem, we need to find the level of output that maximizes total revenue and the level of output that maximizes profits.
a) To maximize total revenue, we need to find the level of output where marginal revenue (MR) is equal to zero. Marginal revenue is the change in total revenue resulting from an additional unit of output. Since revenue is equal to price multiplied by quantity (R = P * Q), marginal revenue can be calculated as the derivative of total revenue with respect to quantity (MR = dR/dQ).
Given the demand function P = 24 - 0.5Q, we can express total revenue as a function of quantity:
R = P * Q = (24 - 0.5Q) * Q = 24Q - 0.5Q^2.
Differentiating total revenue with respect to quantity, we get:
MR = dR/dQ = 24 - Q.
Setting MR equal to zero and solving for Q:
24 - Q = 0
Q = 24.
Therefore, the level of output that maximizes total revenue is Q = 24.
b) To maximize profits, we need to find the level of output where marginal cost (MC) is equal to marginal revenue (MR). Marginal cost is the change in total cost resulting from an additional unit of output. Since cost is equal to average cost multiplied by quantity (C = AC * Q), marginal cost can be calculated as the derivative of total cost with respect to quantity (MC = dC/dQ).
Given the average cost function AC = Q^2 - 8Q + 36 + 3/Q, we can express total cost as a function of quantity:
C = AC * Q = (Q^2 - 8Q + 36 + 3/Q) * Q = Q^3 - 5Q^2 + 36Q + 3.
Differentiating total cost with respect to quantity, we get:
MC = dC/dQ = 3Q^2 - 10Q + 36.
Setting MC equal to MR and solving for Q:
3Q^2 - 10Q + 36 = 24 - Q
3Q^2 - 9Q + 12 = 0.
Factoring the quadratic equation, we get:
(3Q - 4)(Q - 3) = 0.
This equation has two solutions: Q = 4/3 and Q = 3. However, we need to find the positive solution since we cannot have negative quantities.
Therefore, the level of output that maximizes profits is Q = 3.
In summary:
a) The level of output that maximizes total revenue is Q = 24.
b) The level of output that maximizes profits is Q = 3.