Ahealth club currently charges its 1500 clients monthly membership dues of $ 44. 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?

The club should charge $172 to optimize the revenue.

Step-by-step explanation:

Hi there!

The revenue can be calculated as the number of clients times the value of the membership dues. Let y be the revenue, then:

y = 1500 · 44

Let x be the increase in membership dues, then for a increse of x, the number of clients lost will be 5x:

y = (1500 - 5x)(44 + x)

y = 66000 - 220x + 1500x - 5x²

y = -5x² + 1280x + 66000

It is a quadratic equation, a negative parabola. The maximum is the vertex of the parabola that is calculated as:

x = -b/2a

Where:

b = 1280

a = -5

Then:

x = -1280/2 · (-5)

x = 128

The club should charge 44 + 128 = $172 to optimize the revenue.

a4 - 3a2 - 1

step-by-step explanation:

step   1   :

equation at the end of step   1   :

  ((a4) -   3a2) -   1

step   2   :

trying to factor by splitting the middle term

2.1     factoring   a4-3a2-1  

the first term is,   a4   its coefficient is   1 .

the middle term is,   -3a2   its coefficient is   -3 .

the last term, "the constant", is   -1  

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step-by-step explanatio89