Question

The cost per student to attend a school trip is $10.00. At this price, 2000 students will go on the trip. A survey indicates that for every $1 they would lose 100 students. What price per student would result in the greatest revenue.

Answer 1

Let,

cost per student=p

number of students=n

then,

$TR=p \times n$

At p=10, n=2000; $TR=10\times2000=20,000$

At p=11, n=1900; $TR=11\times 1900=20,900$

At p=12, n=1800; $TR=12\times 1800=21,600$

At p=13, n=1700; $TR=13\times 1700=22,100$

At p=14, n=1600; $TR=14\times 1600=22,400$

At p=15, n=1500; $TR=15\times 1500=22,500$

At p=16, n=1400; $TR=16\times 1400=22,400$

the total revenue will increase with increase in cost per student as the number of students decrease.

Therefore, a price of $15.00 per student would result in the greatest revenue.