Mathematics: On Monday Alex earned £120 On Tuesday she earned £100 Alex earned the same amount of money on Wednesday, on Thursday and on Friday She earned a total of £550 for these five days, How much did Alex eam on Wednesday?

On Monday Alex earned £120 On Tuesday she earned

zanaplen27

09.11.2021

The minimum number of hats should company sell to make profit is 401.

Step-by-step explanation:

Given that,

Price of each hat is $ 15.Total Revenue for all hats manufacturing cost is y. it has a y-intercept of 7920 and having a vertex of (150 , 9000) .

To find :

Minimum number of hats the company must sell to make an profit.

From Question:-

Let the number of hats be x.

then total revenue for all hats will be y = 15x

quadratic function given by vertex (h, k) is $y = a(x-h)^{2} + k$

So, using this quadratic function of cost finding the value of (a) we get,

$y = a(x-150)^{2} +9000$

$y = a(x^{2} +22500 - 300x) + 9000$

Now putting the value of y-intercept (0,7920) we get

7920 = a(22500) + 9000

$a= \frac{7920-9000}{22500}$

a= -0.048

Here We know that,

profit = Revenue - cost

$profit = 15x - [0.048(x-150)^{2} + 7920]$

for making profit the above function should be equal to Zero.

$15x - [0.048(x-150)^{2} + 7920] = 0$

$15x = [0.048(x-150)^{2} + 7920]$

$15x = 0.048(x^{2} +22500-300x) + 7920$

$0.048x^{2} + 0.6x -7920 = 0$

solving the quadratic we get the value of x are (401 , - 412.5) So, Neglecting the negative value of x.

Hence the minimum number of hats should company sell to make profit is 401.

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