A bus company has 4000 passengers daily, each paying a a fare of For each each $0.15 increase, the company estimates that it will lose 40 passengers. If the company needs to take in $10 450 per day to stay in business, what fare should be charged?
The revenue must be positive, so if there are x price increases, the revenue is
(4000-40x)(2.00+0.15x)
So, they need
-6x^2+520x+8000 >= 10450
5 <= x <= 81.67
So, the fare must be between $2.75 and $14.25
The maximum revenue of $19270 will be achieved at a price of $8.50
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A bus company has 4000 passengers daily, each paying a fare of $2. For each each $0.15 increase, the company estimates that it will lose 40 passengers. If the company needs to take in $10 450 per day to stay in business, what fare should be charged?
To determine the fare that the bus company should charge, we can work through the problem step by step.
Let's assume that 'x' represents the number of $0.15 fare increases, and 'y' represents the number of passengers lost due to each increase.
We are given that the initial fare is $0.15, and the initial number of passengers is 4000.
According to the information provided, for each $0.15 increase, the company estimates that it will lose 40 passengers. So, the number of passengers lost due to fare increases can be calculated as y = 40x.
Since the company needs to take in $10,450 per day to stay in business, we can calculate the total revenue using the fare and number of passengers. The revenue can be calculated as (4000 - 40x)(0.15 + 0.15x).
Setting up an equation for the revenue, we have:
(4000 - 40x)(0.15 + 0.15x) = 10,450
To solve this equation, we need to simplify it first.
Expanding the equation, we get:
(4000)(0.15) + (4000)(0.15x) - (40x)(0.15) - (40x)(0.15x) = 10,450
Next, simplify the equation:
600 + 600x - 6x - 0.6x^2 = 10,450
Rearrange the terms to form a quadratic equation:
0.6x^2 - 594x + 9,850 = 0
To solve this quadratic equation, you can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a),
where a = 0.6, b = -594, and c = 9,850.
Solve for 'x' using the above formula, and then substitute the value of 'x' back into one of the previous equations, such as y = 40x, to find the number of passengers lost due to fare increases.
Finally, calculate the fare by adding the initial fare of $0.15 to the fare increase (which is equal to $0.15 times the value of 'x').