Mathematics, 11.11.2019 22:31 yen80

Health club currently charges its 1900 clients monthly membership dues of $ 42. the board of directors decides to increase the monthly membership dues. market research shows that each $ 1 increase in dues will result in the loss of 5 clients. how much should the club charge each month to optimize the revenue from monthly dues?

Answers: 3

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Answer from: nina1390

The club should charge $211 to optimize the revenue.

Step-by-step explanation:

Hi there!

The current revenue of the health club is calculated by multiplying the number of clients by the membership due value.

If y = revenue, then:

y = 1900 · 42

So, if the memberiship dues increase by $1, 5 clients will be lost. Then, if the dues increase by a value of x, then the number of lost clients will be 5x. If such an increase is applied, the revenue will be:

y = (1900 - 5x) (42 + x)

Apply distributive property:

y = 79800 + 1900x - 210x - 5x²

y = -5x² + 1690x + 79800

The function is a negative parabola, then, its maximum will be the vertex of the parabola that can be calculated using the following formula:

x = -b/2a

Where:

b = 1690

a = -5

Then:

x = -1690/(2 · -5)

x = 169

The club should charge 169 + 42 = $211 to optimize the revenue.

Answer from: Quest

3/4 ÷ 3/4

step-by-step explanation:

basically divide any proper fraction with itself to fit the criteria.

so if we are using 3/4, then:

3/4 ÷ 3/4 = 1

so 1 is the quotient.

and the numerators for both these fractions is 3. and if we divide the numerators:

3 ÷ 3 = 1

we see that quotient is equal to our original quotient as well.

Answer from: Quest

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2 polynomial long division

dividing : x4+5x3-4x2-8x+6

("dividend")

by : x-1 ("divisor")

dividend x4 + 5x3 - 4x2 - 8x + 6

- divisor * x3 x4 - x3

remainder 6x3 - 4x2 - 8x + 6

- divisor * 6x2 6x3 - 6x2

remainder 2x2 - 8x + 6

- divisor * 2x1 2x2 - 2x

remainder - 6x + 6

- divisor * -6x0 - 6x + 6

remainder 0

quotient : x3+6x2+2x-6 remainder: 0

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Health club currently charges its 1900 clients monthly membership dues of $ 42. the board of directo...