0) Assume the total revenue from the sale of x items is given by R(x) = 31 ln (5x + 1), while the total cost to produce x items is C(x) = x 3 . Find the approximate number of items that should be manufactured so that profit, P(x), is maximum

93 items should be manufacture so that the profit is maximum.

Step-by-step explanation:

Given that,

Total revenue from x items is

R(x)= 31 in (5x+1)

Total cost to produce x items is

Profit = revenue- cost

  P(x)=31 ln (5x+1) -

Differentiating with respect to x

Again differentiating with respect to x

First, we set P'(x) =0

⇒465 - 5x-1 =0

⇒5x= 464

Now

So, at x=93 the profit is maximum.

93 items should be manufacture so that the profit is maximum.

answer: b.

step-by-step explanation:

the y coordinate for point b is 0, and answer b is the only one with that y coordinate.

a_n = a_1 + (n - 1)d

the first term is 6.

the common difference d = ?

when you find d, replace n with 7 and d with the common difference to find your answer.