All 50 rooms in a motel will be rented each night the management charges $65.00 or less per room. For each $10 increase in rent one room will remain vacant. If the cost of maintenance is $15 per room, how much should the management charge in rent to maximize daily profit?
X=# of rooms
profit is rev – cost
R=np (units * cost)
10x = amount of increase
Cost of maintenance=15(50-x)
(65+10x)(50-x)
c=15x
p(x)=(65+10x)(50-x)-15x(50-x)
p(x)=65(50)+50(10x)-x(65)-10(x^2 )-15(50)-15(-x)
p(x)=2500+450x-10x^2
p ?(x)=450-20x
p ?=0 (set to 0)when x=22.5
X=# of rooms
profit is rev – cost
R=np (units * cost)
10x = amount of increase
Cost of maintenance=15(50-x)
(65+10x)(50-x)
c=15x
p(x)=(65+10x)(50-x)-15x(50-x)
p(x)=65(50)+50(10x)-x(65)-10(x^2 )-15(50)-15(-x)
p(x)=2500+450x-10x^2
p ?(x)=450-20x
p ?=0 (set to 0)when x=22.5