A carnival charges $6 for admission and $2.50 per ride. You have $50 to spend at the carnival. Which of the following inequaliti
2 answers:
Answer:
Step-by-step explanation:
Hi!
The options regarding the inequalities are not listed, though we can still proceed to write the inequality.
From the problem statement you cannot spend more than $50
and you are charged admission fee of $6 flat
a ride cost $2.50 per ride
the number of rides is given as r
yet in all you must not go beyond your limit
Therefore the inequalities can be presented as
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Let x be the number of times they raise the price on the newspaper. Then the new cost of the newspaper is
Let y be the newspaper they sell, then the income will be
Now, we know that the circulation is of 500, assuming that they sold every newspaper at the original price now the number the will sell will be
Plugging the value of y in the first expression we have that the income will be
Then the income is given by the function
To find the maximum value of this functions (thus the maximum income) we need to take the derivative of the function,
no we equate the derivative to zero and solve for x.
This means that we have an extreme value of the function when x=9. Now we need to find out if this value is a maximum or a minimum. To do this we need to take the second derivative of the function, then
Since the second derivative is negative in the point x=9, we conclude that this value is a maximum of the function.
With this we conclude that the number of times that they should raise the price to maximize the income is 9. This means that they will raise the price of the newspaper (9)($0.05)=$0.45.
Therefore the price to maximize the income is $0.35+$0.45=$0.80.