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AleksAgata [21]
3 years ago
6

Profit is the difference between revenue and cost. The revenue, in dollar, of company that manufactures television can be modele

d by the polynomial 3x²+180x. The cost,in dollar, of producing the televisions can be modeled by 3x²-160x+300.The variable x is the number of televisions sold. If 150 televisions are sold ,what is the profit?
C)$50,700​
Mathematics
1 answer:
Anon25 [30]3 years ago
3 0

Answer:

The profit in this case is equal to $50,700.

Step-by-step explanation:

As the problem stated profit is the difference between revenue and cost, in this case we have:

revenue(x) = 3x^2 + 180x

cost(x) = 3x^2 - 160x + 300

So the profit will be the difference between these two functions.

profit(x) = revenue(x) - cost(x)\\profit(x) = 3x^2 + 180x - 3x^2 + 160x - 300\\profit(x) = 340x - 300

In order to find the profit when 150 televisions are sold we need to make x equal 150.

profit(150) = 340*150 - 300\\profit(150) = 51000 - 300 = 50700

The profit in this case is equal to $50,700.

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<u>Step-by-step explanation:</u>

Here we have ,  f(x) = x² - 2x + 7 or f(x) = x^2 - 2x + 7 . We need to find the minimum value of f(x) for which we need to differentiate it one time and equate it to zero . Value of x at which first differentiation of f(x) is zero will be the minimum value of function  . Let's solve this:

f(x) = x^2 - 2x + 7

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⇒ \frac{df(x)}{dx} = \frac{d(x^2 - 2x + 7)}{dx}

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⇒ \frac{df(x)}{dx} = 2x-2 = 0

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Therefore, minimum value of the quadratic function f(x) = x² - 2x + 7 is at x=1 & is (1, 6).

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