A travel agency organized a group to travel to other places. 20 people formed a group together, and the unit price per person was 1,200 yuan. If there are more than 20 people in each group, discounts

A travel agency organized a group to travel to other places. 20 people formed a group together, and the unit price per person was 1,200 yuan. If there are more than 20 people in each group, discounts will be given. For each additional person,

①If there are no more than 20 people, the turnover y=1200x,

When x=20, y reaches the maximum, and the maximum value is 24,000 yuan;

②If there are more than 20 people, the discounted unit price is 20×(x-20)=20x-400,

Then y=[1200-(20x-400)]x=-20x2+1600x=- 20(x-40)2+32000,

When x=40, y obtains the maximum, and the maximum y=32,000 yuan.

To sum up, the number of people per group is 40 hours, which is the maximum turnover that the travel agency can obtain.

Answer: When the number of people per group is 40, the travel agency can obtain the maximum turnover.

(2) Suppose the profit is w, then

①If there are no more than 20 people, then w=y-Q=1200x-6x2-18000=-6(x-100)2+ 42000,

When x=20, w reaches the maximum, wmax=3600 yuan;

②If there are more than 20 people, then w=y-Q=-20x2+1600x-(6x2 +18000)=-26x2+1600x-18000=-26(x-40013)2+6615.4,

∵x is an integer,

∴When x=31, w is obtained maximum.

To sum up, it can be concluded that when the number of people in each group is 31, the profit will be the largest.

Answer: In order to obtain the maximum profit, it is most suitable to have 31 people in each group.