Question

The​ profit, in thousands of​ dollars, from the sale of x thousand candles can be estimated by ​P(x) = 5 x - 0.7 x ln x.

Answer 1

Answer:

1). Marginal profit= P'(x) = 5+ 0.7(Inx +1)

2) P'(10)= 3.23121

A. The additional profit, in thousands of dollars, for selling a thousand candles once 10,000 candles have already been sold.

Step-by-step explanation:

​P(x) = 5 x - 0.7 x ln x.

P'(x) = differential of ​P(x) = 5 x - 0.7 x ln x.

Differential of 5x= 5

Differential of xInx = Inx +1

P'(x) = 5+ 0.7(Inx +1)

Marginal profit= P'(x) = 5+ 0.7(Inx +1)

For P'(10)

P'(x) = 5- 0.7(Inx +1)

P'(10)= 5-0.7(In10 +1)

P'(10)=5-0.7(2.303 +1)

P'(10)=5-0.7(3.303)

P'(10)=5- 2.3121

P'(10)= 3.23121

If ​P(10) = 5 x - 0.7 x ln x.

P(10) = 50-0.7(10)(In10)

P(10)= 50-16.12

P(10)= 33.88