8) A travel agent is proposing a tour in which a group will travel in a plane of capacity 150. The fare will be
*1400 per person if 120 or fewer people go on the tour, but the fare for each person will be decreased by
10 for each person in excess of 120, if the total number of traveler exceeds 120. For example, if there are
125 traveler, then the fare for each will be 1400 - ₹10(5) = 1350. Let x represents the number of
people going on the tour. What will be the value of for which the income of the travel agent will be
maximum from this tour?
Answers
Given : A travel agent is proposing a tour in which a group will travel in a plane of capacity 150. The fare will be *1400 per person if 120 or fewer people go on the tour, but the fare for each person will be decreased by
10 for each person in excess of 120,
To Find : What will be the value of traveler for which the income of the travel agent will be maximum from this tour
Solution:
Let say x will be traveler over and above 120
Total traveler = 120 + x
income of the travel agent (120 + x)( 1400 - 10x)
where 0 ≤ x ≤ 30 as max capacity = 150
(120 + x)( 1400 - 10x)
= 120(1400) - 1200x + 1400x - 10x²
= 168000 +200x - 10x²
Taking derivative wrt x
200 - 20x
=> 200 - 20x = 0 => x = 10
Taking derivative wrt x again
= - 20 < 0 hence x = 10 will give maximum value
x = 10
120 + 10 = 130 Traveler
income = 130 x ( 1400 - 10 * 10)
= 130 x 1300
= 169000 Rs
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