Business: Profit Suppose that the daily profit (in dollars) from the production and sale of x units of a product is given byP180xx210002000At what rate per day is the profit changing when the number of units produced and sold is 100 and is increasing at a rate of 10 units per day

Absolutely not, i fw you for trying tho...

Profit Suppose that the daily profit (in dollars)

Ответ:

tinsey

25.06.2021

Business

The answer is "1798".

Explanation:

$\to p=180x-\frac{x^{2}}{1000}-2000$

In order to find the rate of profit increase each day, we differentiate between the money demand function and the time t.

$\to \frac{dp}{dt}=180\frac{dx}{dt}-\frac{2x}{1000}\frac{dx}{dt} \\\\\to \frac{dp}{dt}=\frac{dx}{dt}\left (180-\frac{2x}{1000} \right ).................(1)$

Calculate $\frac{dp}{dt}$ when x=100

$\frac{dx}{dt}=10$ (Extension rate of produced and delivered units per day)

$x=100 \ and\ \frac{dx}{dt}=10 ......... in \ \ eq(1)\\\\\frac{dp}{dt} = 10\left (180-\frac{2(100)}{1000} \right )\\\\$

$=10\left (180-0.2\right ) \\\\=1798 \\\\$

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Profit Suppose that the daily profit (in dollars) from the production and sale of x units of a product is given byP180xx210002000At what rate per day is the profit changing when the number of units produced and sold is 100 and is increasing at a rate of 10 units per day

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