g A gift shop sells 40 wind chimes per month at $110 each. The owners estimate that for each $11 increase in price, they will sell 2 fewer wind chimes per month. Find the price per wind chime that will maximize revenue.

The price that maximizes the revenue is $165

Step-by-step explanation:

We can model the price as a function of sold units as a linear relationship.

Remember that a linear relationship is something like:

y = a*x + b

where a is the slope and b is the y-intercept.

We know that if the line passes through the points (x₁, y₁) and (x₂, y₂), then the slope can be written as:

a = (y₂ - y₁)/(x₂ - x₁)

For this line, we have the point (40, $110)

which means that to sell 40 units, the price must be $110

And we know that if the price increases by $11, then he will sell 2 units less.

Then we also have the point (38, $121)

So we know that our line passes through the points (40, $110) and  (38, $121)

Then the slope of the line is:

a = ($121 - $110)/(38 - 40) = $11/-2 = -$5.5

Then the equation of the line is:

p(x) = -$5.5*x + b

to find the value of b, we can use the point (40, $110)

This means that when x = 40, the price is $110

then:

p(40) = $110 = -$5.5*40 + b

            $110 = -$220 + b

       $110 + $220 = b

        $330 = b

Then the price equation is:

p(x) = -$5.5*x + $330

Now we want to find the maximum revenue.

The revenue for selling x items, each at the price p(x), is:

revenue = x*p(x)

replacing the p(x) by the equation we get:

revenue = x*(-$5.5*x + $330)

revenue = -$5.5*x^2 + $330*x

Now we want to find the x-value for the maximum revenue.

You can see that the revenue equation is a quadratic equation with a negative leading coefficient. This means that the maximum is at the vertex.

And remember that for a quadratic equation like:

y = a*x^2 + b*x + c

the x-value of the vertex is:

x = -b/2a

Then for our equation:

revenue = -$5.5*x^2 + $330*x

the x-vale of the vertex will be:

x = -$330/(2*-$5.5) = 30

x = 30

This means that the revenue is maximized when we sell 30 units.

And the price is p(x) evaluated in x = 30

p(30) = -$5.5*30 + $330 = $165

The price that maximizes the revenue is $165

a line is an defined derm because it

a)contains an infinite number of points b) can be used to create other geometric shapes c)describes something that does not have width or depth d) is a term that does not have a formal definition. a line is an undefined term because it: contains an infinite number of points.

1,8,15,22,29,36,43,50

step-by-step explanation: