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3 years ago

La deltamath.com/app/student/solve/13663622/custom1610392117456

Mathematics

1 answer:

klasskru [66]3 years ago

5 0

Answer:

See explanation

Step-by-step explanation:

The question is incomplete as the required trapezoid is not given. SO, I will answer using genera rules.

The area of a trapezoid is:

$Area = \frac{1}{2}(x + y) * z$

Where

$x, y \to$ parallel sides

$z \to height$

Assume that:

$x = 2; y =3; z = 4$

The formula becomes

$Area = \frac{1}{2} * (2 + 3) * 4$

$Area = \frac{1}{2} * 4 * 4$

$Area = 5$

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The manager of a company uses the function shown to model the company’s daily profit based on the price of a product in dollars,

just olya [345]

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2) the maximum price in dollars , to avoid a loss = 53,

3) The price that results the maximum profit = 37.5 dollars

Step-by-step explanation:

Since the given function that shows the total profit,

$f(x) = (x-22)(53-x)$

Where x is the price of the product.

Since for avoiding the loss,

$f(x) \geq 0$ ,

⇒ $(x-22)(53-x)\geq 0$

If $(x-22)\geq 0 \implies x\geq 22$

If $53 - x \geq 0 \implies 53 \geq x$

Thus, 53 ≥ x ≥ 22,

Therefore, the minimum price to avoid the loss = $ 22

And, the minimum price to avoid the loss = $ 53

$f'(x) =\frac{d}{dx}[(x-22)(53-x)] = (x-22)\frac{d}{dx} (53-x)+(53-x) \frac{d}{dx}(x-22)$

⇒ $f'(x) = - (x-22)+(53-x) = -x+22+53-x =-2x+75$

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$f'(x) = 0$ ,

⇒ $-2x+75 = 0$

⇒ $-2x = -75$

⇒ $x = 37.5$

$f''(x) = \frac{d}{dx}(-2x+75)=-1$

For x = 37.5, f''(x) is negative,

Thus, For the price of $ 37.5 dollars the company has the greatest profit.

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