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.
Answer: they have 68 servings of ice cream left for the party
Step-by-step explanation:
The Smiths purchased 6 containers of ice cream for a party. Each container holds 9 cups of ice cream. This means that the total number of cups of ice cream that they have is
6 × 9 = 54 cups
Before the party, their sons ate 3 cups of ice cream altogether. This means that the number of cups of ice cream that they have left is
54 - 3 = 51 cups
One serving is 3/4 cup of ice cream. This means that the number of serving that they have left is
51/0.75 = 68
Answer:
The shortest sides is 3x-10
Step-by-step explanation:
This is because if you do the algebra which is 4x+3+2x+8+3x-10=136, x=15. Now that you have 15 you plug it into each sides x value. First, 4x+3= 4*15+3=63
Second, 2x+8=30+8=38
Lastly, 3x-10=45-10=35
So, as you can see here 35 is the lowest value which means the side (3x-10) is the shortest.