A firm’s total revenue function and total cost function are as follows:TR = 200Q – Q2TC = 50 + 20Q +0.5Q2Use this information the answer the following three questions (Q16-Q18).To maximize total revenue, how much quantity should the firm produce?a.Q = 200b.Q = 100c.Q = 150d.Q = 50To minimize average cost, how much quantity should the firm produce?a.Q = 20b.Q = 10c.Q = 100d.Q = 200To maximize profit, how much quantity should the firm produce? a.Q = 40b.Q = 80c.Q = 60d.Q = 20

1. To maximize total revenue, we need to find the quantity (Q) that maximizes the total revenue function (TR = 200Q - Q^2). This is done by taking the derivative of the total revenue function with respect to Q, setting it equal to zero, and solving for Q.

The derivative of TR = 200Q - Q^2 is 200 - 2Q. Setting this equal to zero gives:

200 - 2Q = 0 2Q = 200 Q = 100

So, the firm should produce 100 units to maximize total revenue. The correct answer is (b) Q = 100.

2. To minimize average cost, we first need to find the average cost function. Average cost (AC) is total cost (TC) divided by quantity (Q). So, AC = (50 + 20Q + 0.5Q^2) / Q = 50/Q + 20 + 0.5Q.

To find the quantity that minimizes average cost, we take the derivative of the average cost function with respect to Q, set it equal to zero, and solve for Q.

The derivative of AC = 50/Q + 20 + 0.5Q is -50/Q^2 + 0.5. Setting this equal to zero gives:

-50/Q^2 + 0.5 = 0 50/Q^2 = 0.5 Q^2 = 100 Q = 10

So, the firm should produce 10 units to minimize average cost. The correct answer is (b) Q = 10.

3. To maximize profit, we need to find the quantity (Q) that maximizes the profit function. Profit is total revenue (TR) minus total cost (TC), so Profit = (200Q - Q^2) - (50 + 20Q + 0.5Q^2) = 180Q - 1.5Q^2 - 50.

Taking the derivative of the profit function with respect to Q, setting it equal to zero, and solving for Q gives:

180 - 3Q = 0 3Q = 180 Q = 60

So, the firm should produce 60 units to maximize profit. The correct answer is (c) Q = 60.