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The profit-maximizing price and quantity are calculated below:

$$\begin{gathered} \text{P = 500 - Q} \\ \text{MR = 500 - 2Q} \\ \text{MC = \$ 100} \\ \text{MR = MC} \\ \text{500 - 2Q = 100} \\ \text{2Q = 400} \\ \text{Q = 200} \\ \text{P = 500 - 200} \\ \text{= \$ 300} \end{gathered}$$

The price will be $300 per ticket and 200 people on each flight.

The total profit is calculated below:

$$\begin{gathered} \mathrm{蟺}=\left(300脳200\right)-30,000-100\left(200\right) \\ =60,000-30,000-20,000 \\ =\$10,000 \end{gathered}$$

The total profit will be $10,000.

As the fixed cost increases, it will not alter the output level and the price, as the fixed cost does not enter into the marginal cost. With the increase in fixed cost, only the profit reduces. EA cannot shut down immediately as the fixed cost will be more. The shutdown will happen only when the earnings cannot pay the fixed cost.

The graph below shows the change in average cost:

AC₁ represents when the average cost when FC is $30,000, and AC₂ represents when the average cost when FC is $41,000. Here, the average cost is $250 when the FC is $30,000, and the average cost is $305 when the FC is $41,000; $300 represents the price per ticket.

The price and quantity of Type A customers are calculated below:

$$\begin{gathered} {\text{Q}}_{\text{A}}{\text{= 260 - 0.4P}}_{\text{A}} \\ {\text{P}}_{\text{A}}{\text{= 650 - 2.5Q}}_{\text{A}} \\ {\text{MR}}_{\text{A}}{\text{= 650 - 5Q}}_{\text{A}} \\ \text{MC = 100} \\ {\text{650 - 5Q}}_{\text{A}}\text{= 100} \\ {\text{5Q}}_{\text{A}}\text{= 550} \\ {\text{Q}}_{\text{A}}\text{= 110} \\ {\text{P}}_{\text{A}}\text{= 650 - 2.5}\left(\text{110}\right) \\ \text{= 650 - 275} \\ \text{= \$ 375} \end{gathered}$$

There will be 110 business passengers at a ticket price of $375.

The price and quantity of Type B customers are calculated below:

$$\begin{gathered} {\text{Q}}_{\text{B}}{\text{= 240 - 0.6P}}_{\text{B}} \\ {\text{P}}_{\text{B}}{\text{= 400 - 1.667Q}}_{\text{B}} \\ {\text{MR}}_{\text{B}}{\text{= 400 - 3.33Q}}_{\text{B}} \\ \text{MC = 100} \\ {\text{400 - 3.33Q}}_{\text{B}}\text{= 100} \\ {\text{3.33Q}}_{\text{B}}\text{= 300} \\ {\text{Q}}_{\text{B}}\text{= 90} \\ {\text{P}}_{\text{B}}\text{= 400 - 1.667}\left(\text{90}\right) \\ \text{= 400 - 150} \\ \text{= \$ 250} \end{gathered}$$

There will be 90 student passengers at a ticket price of $250.

The demand curve is shown below:

The price charged to passenger A is higher than that changed for passenger B. Passenger A will have a steep demand curve due to inelastic demand, and passenger B will have a flat demand curve; hence, the demand curve is flat from $400 onwards but steep till $400.

The profit is calculated below:

$$\begin{gathered} \mathrm{蟺}=\left(250脳90\right)\left(375脳110\right)-41,000-100\left(90+110\right) \\ =22,500+41,250-41,000-20,000 \\ =\$2750 \end{gathered}$$

Yes, the airline will stay in business as the profit is positive.

The consumer surplus for both types of the consumer is calculated below:

$$\begin{gathered} C{S}_A=0.5脳110脳\left(650-375\right) \\ =0.5脳110脳275 \\ =\$15,125 \\ C{S}_B=0.5脳90脳\left(400-250\right) \\ =0.5脳90脳150 \\ =\$6,750 \end{gathered}$$

The total consumer surplus will be $21,875 (=15,125 + 6750).

When the price is $300, then the consumer surplus for Type A customers will be,

$$\begin{gathered} Q_A=260-0.4\left(300\right) \\ =260-120 \\ =140 \\ CS=0.5脳140\left(650-300\right) \\ =0.5脳140-350 \\ =\$24,500 \end{gathered}$$

When the price is $300, then the consumer surplus for Type B customers will be,

$$\begin{gathered} Q_B=240-0.6\left(300\right) \\ =240-180 \\ =60 \\ CS=0.5脳60\left(400-300\right) \\ =0.5脳60-100 \\ =\$3,000 \end{gathered}$$

The total consumer surplus will be $27500, which is greater than the consumer surplus with the price discrimination. The difference in consumer surplus is that the business consumer has to pay more during the price discrimination, and their demand is inelastic.