Ticket price expand your wings airlines finds that if it...

Ticket price Expand Your Wings Airlines finds that if it prices a Los Angeles to New York one-way ticket at $390, it can sell 350 seats on its airplane . The airline estimates that for each $10 price reduction. per ticket, 25 more tickets can be sold each day. The cost to the airline for each ticket is $150. Find the price at which the airline should sell a ticket to maximize its daily profit on ticket sales for the Los Angeles to New York flight.

Transcript

00:02 A airliner find that prices to la to new york for a one -way ticket is $390 and they can sell 350 tickets.

00:10 They realize if they decrease the price by $10, they'll sell 25 more tickets.

00:17 So let's see how much their revenue would be for that.

00:20 So that we need to let x be the number of $10 reductions.

00:28 That's not the number of tickets, but the number of $10 reductions.

00:32 So that means we're going to go 390 minus 10 times x.

00:38 And that's going to mean that we're going to have 350 plus 25 times x, because for each $10 reduction, it increases by 25.

00:50 So that means my revenue then is going to be 390 minus 10x, the cost of the ticket, times 350 plus 25x, the number of tickets.

01:02 Now it tells us that the cost for each ticket to the airline is 150.

01:07 So we have our cost.

01:08 It's going to be 150 per ticket.

01:12 Well, how many tickets are they selling? not x, that's the number of reductions.

01:17 It's going to be 350 plus 25x.

01:22 So we now need to find our profit.

01:24 Profit is going to be revenue minus cost, which is going to be 390 minus 10x, times 350 plus 25x minus our cost, which is 150 times 350 plus 25 x.

01:42 Let's simplify this.

01:44 I've noticed that these two terms have a greatest common factor of 350 plus 25x.

01:50 That's going to make our life a little bit easier because now it's being multiplied by 390 minus 10x minus 150, which would become 350 plus 25x...

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