A company plans to sell embroidered hats for $15 eachThe company's financial planner estimates that the cost, y, of manufacturing the hats is a quadratic function with a y-intercept of 7,920 and a vertex of (150, 9,000)What is the minimum number of hats the company must sell to make a profit?

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

quadratic function given by vertex (h, k) is

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

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

Here We know that,

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

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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step-by-step explanation:

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