the profit of a certain company is given by p(x)=10,000+350x-1/2xsq where x is the amount (birr in tens) spent on advertising. Whate amount gives a profit of more than birr 40,000?

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Well, based on the given profit function, we can set it to be greater than 40,000 and solve for x.

10,000 + 350x - 1/2x^2 > 40,000

To make things simpler, let's multiply both sides by 2 to get rid of the fraction:

20,000 + 700x - x^2 > 80,000

Next, let's rearrange the equation to have zero on one side:

x^2 - 700x + 60,000 < 0

Now we have a quadratic inequality. To find the values of x that satisfy this inequality, we can either solve it algebraically or use graphical methods.

Or, you could hire a professional comedian to solve this for you, because bringing humor to math can make it much more enjoyable!

To find the amount x that gives a profit of more than 40,000 birr, we need to solve the inequality p(x) > 40,000.

Given that p(x) = 10,000 + 350x - (1/2)x^2, we can rewrite the inequality as:

10,000 + 350x - (1/2)x^2 > 40,000

Rearrange the terms:

- (1/2)x^2 + 350x + 10,000 - 40,000 > 0

Combine like terms:

- (1/2)x^2 + 350x - 30,000 > 0

To solve this quadratic inequality, we can factor it. First, multiply all terms by -2 to simplify the equation:

x^2 - 700x + 60,000 < 0

Next, factor the quadratic equation:

(x - 400)(x - 300) < 0

Now, we have two critical points where the equation equals zero: x = 300 and x = 400.

Plot these points on a number line as open circles:

----o----o----

Now, choose a test point from each interval formed by these critical points and plug it into the inequality to determine which intervals satisfy the inequality. Let's choose x = 350 (midpoint between 300 and 400):

(350 - 400)(350 - 300) < 0
(-50)(50) < 0
-2500 < 0

Since this test point satisfies the inequality, the interval (300, 400) is part of the solution.

Therefore, the amount x that gives a profit of more than 40,000 birr is any value between 300 and 400 (exclusive), in tens.

To find the amount (in tens of birr) that gives a profit of more than 40,000 birr, we need to solve the inequality p(x) > 40,000.

Given that p(x) = 10,000 + 350x - 1/2x^2, we can rewrite the inequality as:

10,000 + 350x - 1/2x^2 > 40,000

First, let's rearrange the equation to get it in quadratic form:

-1/2x^2 + 350x + 10,000 > 40,000

Next, let's move all the terms to the left side to set the quadratic equation to zero:

-1/2x^2 + 350x + 10,000 - 40,000 > 0

Simplifying further:

-1/2x^2 + 350x - 30,000 > 0

Now, to solve this inequality, we can use various methods such as factoring, graphing, or the quadratic formula. Since this quadratic equation might not factor easily, let's use the quadratic formula to find the solutions:

x = (-b ± √(b^2 - 4ac))/(2a)

In this case, a = -1/2, b = 350, and c = -30,000. Substituting these values into the quadratic formula:

x = (-(350) ± √((350)^2 - 4(-1/2)(-30,000))) / (2(-1/2))

Simplifying further:

x = (-350 ± √(122,500 + 60,000)) / -1

x = (-350 ± √(182,500)) / -1

Now, we have two potential solutions:

x1 = (-350 + √(182,500)) / -1
x2 = (-350 - √(182,500)) / -1

Calculating these values:

x1 ≈ -24.77
x2 ≈ 374.77

Since we are dealing with advertising amounts, which should be positive, we can discard the negative value of x1.

Therefore, the amount that gives a profit of more than 40,000 birr is approximately 374.77 birr (in tens).