The table is missing though but you may consider the following calculations :
Y = 1.6 x
for x = 1 minutes
Y = 1.6 laps
for x = 2 minutes
Y = 3.2 laps
for x = 3 minutes
Y = 4.8 laps
The angles of a triangle always add up to 180°.
120 + x + 16 + x = 180
Add up the values.
136 + 2x = 180
Subtract 136 from both sides.
2x = 44
Divide both sides by 2.
x = 22
Answer:
55
Step-by-step explanation:
This is 55 because you need to make a sum of 180 when making a line and 125+55=180
A) Demand function
price (x) demand (D(x))
4 540
3.50 810
D - 540 810 - 540
----------- = -----------------
x - 4 3.50 - 4
D - 540
----------- = - 540
x - 4
D - 540 = - 540(x - 4)
D = -540x + 2160 + 540
D = 2700 - 540x
D(x) = 2700 - 540x
Revenue function, R(x)
R(x) = price * demand = x * D(x)
R(x) = x* (2700 - 540x) = 2700x - 540x^2
b) Profit, P(x)
profit = revenue - cost
P(x) = R(x) - 30
P(x) = [2700x - 540x^2] - 30
P(x) = 2700x - 540x^2 - 30
Largest possible profit => vertex of the parabola
vertex of 2700x - 540x^2 - 30
When you calculate the vertex you find x = 5 /2
=> P(x) = 3345
Answer: you should charge a log-on fee of $2.5 to have the largest profit, which is $3345.
