help please A travel agency will plan a tour for groups of s

help please

A travel agency will plan a tour for groups of size 25 or more. If the group contains exactly 25 people, then the price of the tour is $500 per person. However, the price per person is reduced by $10 for each additional person above 25 that books the tour. If the travel agency incurs a cost of $130 per use calculus techniques to determine what size group will maximize the agencies profit? Be certain to prove that your answer yields the maximum possible revenue.

Solution

as per given data:

       For 25 persions book the tour need $500 per each

       if add any one then $10 less per each

       i,e For 26 persions book the tour need $490 per each

       if travel agency got $130 per each then member=?

           if difference for 1 persion to $10

             then how many persions to$500-$130=$370

             for 37 persions to$500-$130=$370

   total 37+25=62 persion pay each $130 for travels to book tour.

   total agency profit=62*130=8060.