Question

Question is in screenshot. Please answer it correctly

Answer 1

a) You need to sell 12 or 29 dresses.

b) Any number between 2 and 39 dresses will give a positive profit.

How many dresses must be sold in order to make a profit of 3000 euros?

Here we know that the profit, in euros, as a function of the number of dresses sold is:

P(x) = -11*x^2 + 450*x - 800

Now, if you want to find how many dresses you need to sell to have a profit of 3000 euros, then you need to solve:

P(x) = 3000 = -11*x^2 + 450*x - 800

So we need to solve the quadratic equation:

-11x^2 + 450x - 800 - 3000 = 0

-11x^2 + 450x - 3800 = 0

The solutions are given by Bhaskara's formula:

x = (-450 ± √(450^2 - 4*(-3800)*(-11))/2*(-11)

x = (-450 ± 187.9)/(-22)

We have two solutions that give the same profit:

• x = (-450 + 187.9)/-22 = 11.9 that can be rounded to 12.
• x = (-450 - 187.9)/-22 = 28.99 that can be rounded 29.

Then if you sell either 12 or 29 dresses, you will get a profit of 3000 euros.

b) To make a profit you need to sell more than P = 0, so let's solve that first:

P= 0 = -11*x^2 + 450*x - 800

The solutions are:

x = (-450  ± √(450^2 - 4*(-800)*(-11))/2*(-11)

x = (-450  ± 409)/(-22)

The smaller solution is:

x = (-450 + 409)/-22 = 1.86 that can be rounded to 2.

(because you can't sell 1.86 of a dress)

The other solution is:

x =  (-450 - 409)/-22 = 39

So, between 2 and 39 dresses, you will make a profit.

If you want to learn more about quadratic equations:

brainly.com/question/1214333

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