[From: ] [author: ] [Date: 12-06-02] [Hit: ]
the company has to increase the ticket price by \$5. Explain how to determine the number of empty seats that the bus should run in order to maximize profit.Can someone help me with this question??? Please and thankyou!......
it costs a bus company \$225 to run a minibus on a ski trip plus \$30 per. passenger. The bus has seating capacity for 22 people. The company charges \$60 per fare if the bus is full. For each empty seat, the company has to increase the ticket price by \$5. Explain how to determine the number of empty seats that the bus should run in order to maximize profit.

Can someone help me with this question??? Please and thankyou!~

-
Cost= C= 225+30x , Where x = number of passengers:
x = 22-n Where n= number of empty seats

C= 225+30(22-n)

C= 885-30n

Now for revenue, a full bus is 60 dollars for each of 22 passengers= 60(22)
But with n empty seats, number of passengers is 22-n, and price is 60+ 5n

Revenue = R= (60+5n)(22-n)

R= 1320+ 50n -5n^2

Profit= P= R- C = (1320+50n -5n^2 ) - (885-30n)

P= -5n^2 + 80n + 435

Notice this is a parabola that opens down, so the maximum occurs at the vertex.

n= -b/(2a)= -80/(2*-5)= 8

There should be 8 empty seats to maximize profit.

Hoping this helps!
1