SOLUTION: Dilan, a high school student, provides lawn-cutting services during his summer vacation. In the past, he has averaged 25 clients a week, charging $8 per lawn. After conducting a n

Algebra ->  Triangles -> SOLUTION: Dilan, a high school student, provides lawn-cutting services during his summer vacation. In the past, he has averaged 25 clients a week, charging $8 per lawn. After conducting a n      Log On


   

Question 1190011: Dilan, a high school student, provides lawn-cutting services during his summer vacation. In the past,
he has averaged 25 clients a week, charging $8 per lawn. After conducting a neighborhood survey,
Dilan realizes that for every $2 increase in price for lawn-cutting, he expects to lose 2 clients.
Determine how much he should charge per lawn to maximize his revenue.
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
2x= 2 clients and $2
x=1 fewer client and $1 more dollar per lawn.
currently 25 clients*$8/client or $200.
(25-x)($8+x)=200+17x-x^2
This is maximum at the vertex of -b/2a=-17/-2 or 8.5
has 25-8.50 or 16.5 customers
charges $16.50 per lawn
$276.38
has to be 16 or 17 customers.
16 would charge $17 for $272
17 would charge $16 for the same, $272
graph%28300%2C300%2C-20%2C20%2C-50%2C300%2C-x%5E2%2B17x%2B200%29
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can check
23 clients with $10 ($230)
21 with with $12 ($252)
19 with $14 ($266)
17 with $16 ($272)
15 with $18 (270)
13 with $20 (260)