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.
1) Find the marginal profit, P'(x).
2) Find P'(10), and explain what this number represents. What does P'(10) represent?
A. The additional profit, in thousands of dollars, for selling a thousand candles once 10,000 candles have already been sold.
B. The additional profit, in thousands of dollars, when 10,000 candles are sold.
C. The additional cost, in thousands of dollars, to produce a thousand candles once 10,000 candles have already been sold.
D The additional cost, in thousands of dollars, to produce 10,000 candles.
C. How many thousands of candles should be sold to maximize profit?

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