Airlines has a flight scheduled to leave. They have currently sold 320 tickets a

Question

Airlines has a flight scheduled to leave. They have currently sold 320 tickets at a price of $600. The plane has a capacity of 400 passengers leaving 80 seats unsold. They would like you to determine the lowest super saver fare they could charge for the remaining 80 seats without affecting their current profit of flying 320 passengers (the breakeven price for the remaining 80 seats). Given the following revenue and cost equations:

P=760-.5Q

TR=760Q-.5Q (squared)

TC=20,000+6Q+.5Q (squared)

MC=6+Q

MR=760-Q

A. Determine the lowest super saver fare per passanger they could charge. Show your work.

Explanation / Answer

when Q= 320

profit = TR - TC

= 760Q - 0.5Q^2 - 20000 - 6Q - 0.5Q^2

= 754 Q - Q^2 - 20000

= 118880

and for remaining 80 seats TR = TC then there would be no extra profit

760Q - 0.5Q^2 = 20000 + 6Q + 0.5Q^2

Q^2 - 754 Q +20000 = 0

solving quadratic equation we get , Q = 728

p = 760 - 0.5 * 728 = 396

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