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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?
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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?
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?
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
(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
8 answers