Question

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

Answer 1

The answer is "1798".

Step-by-step explanation:

`\to p=180x-(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 (dp)/(dt)=180(dx)/(dt)-(2x)/(1000)(dx)/(dt) \\\\\to (dp)/(dt)=(dx)/(dt)\left (180-(2x)/(1000) \right ).................(1)`

Calculate
`(dp)/(dt)` when
`x=100`

`(dx)/(dt)=10` (Extension rate of produced and delivered units per day)

`x=100 \ and\ (dx)/(dt)=10 ......... in \ \ eq(1)\\\\(dp)/(dt) = 10\left (180-(2(100))/(1000) \right )\\\\`

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