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.
An exterior angle is equal to the sum of the two opposite inside angles.
T + 31 = t + t-29
Simplify:
T + 31 = 2t -29
Add 29 to both sides:
T + 60 = 2t
Subtract 1t from both sides:
T = 60
If C is between A and B, then, we can write the equation
Substitute the value of AB and the expressions for AC and CB in terms of x.
We can now solve for x.
Dividing by 5.
Answer:
390 miles
Step-by-step explanation:
