Find the level of production x that will maximize the profit...

Name: Find the level of production x that will maximize the profit of a company given the following data. The weekly demand equation is p = -2x + 6 and the cost function is C(x) = x³ - 4x² + x + 6.
Uploaded: 2023-05-02T13:36:35-08:00
Duration: 5 min 9 s
Channel: Madhur L
Description: Find the level of production x that will maximize the profit of a company given the following data. The weekly demand equation is p = -2x + 6 and the cost function is C(x) = x³ - 4x² + x + 6.

Find the level of production x that will maximize the profit of a company given the following data. The weekly demand equation is p = -2x + 6 and the cost function is C(x) = x³ - 4x² + x + 6.

Transcript

00:01 Hello, here we have a given that a demand equation.

00:03 So, we have a demand equation as that is p of x is equal to minus 2x plus 6.

00:10 Now, we can write and also we have a given that is a cost function that is c of x is equal to x cube minus of 4x square plus x plus 6.

00:23 Now, let's suppose a of x be the profit function.

00:31 So, this is the profit function.

00:39 So, now from here we can write it as a of x is equal to x multiplied by that is demand equation which is given as p of x.

00:48 Now, minus of the cost function that is c of x.

00:52 Now, putting the value from here we have x multiplied by minus of 2x plus 6 minus of cx that is x cube minus of 4x square plus x plus 6.

01:06 Now, solving from here we can write it as that is minus of x cube plus 2x square plus 5x minus of 6.

01:16 Now, we got the value of a of x.

01:19 Now, differentiating with respect to x.

01:20 So, we have a dash of x that is equal to minus of 3x square plus 2 multiplied by 2 that is 4x.

01:29 Now, plus of 5 by using the differentiated formula as that is b divided by d of x, x to the power n which is equal to nx n minus 1.

01:39 Now, from here we got a dash x.

01:42 Now, again differentiating with respect to x we have a double dash x that is equal to minus of 6x plus 4.

01:50 Now, for the maximum and the minimum value we have that is a dash x is equal to 0.

01:58 So, for this we can write that minus of 3x square plus 4x plus 5 is equal to 0.

02:05 Now, here we can see that this is the quadratic equation...

Question

Find the level of production x that will maximize the profit of a company given the following data. The weekly demand equation is p = -2x + 6 and the cost function is C(x) = x³ - 4x² + x + 6.

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