The profit, in thousands of dollars, from the sale of x thousand candles can be
ID: 2887220 • Letter: T
Question
The profit, in thousands of dollars, from the sale of x thousand candles can be estimated by P(x) = 3x-0.5x in x. Complete parts (a) through (c). a) Find the marginal profit, P' (x). b) Find P (25), and explain what this number represents. P'(25) Type an integer or decimal rounded to the nearest thousandth as needed.) What does P (25) represent? O A. The additional profit, in thousands of dollars, for selling a thousand candles once 25,000 candles have already been sold O B. The additional profit, in thousands of dollars, when 25,000 candles are sold. O C. The additional cost, in thousands of dollars, to produce a thousand candles once 25,000 candles have already been sold. O D. The additional cost, in thousands of dollars, to produce 25,000 candles. c) How many thousands of candles should be sold to maximize profit? (Type an integer or decimal rounded to the nearest thousandth as needed.)Explanation / Answer
P(x) = 3x-0.5x ln x
a. Marginal profit, P'(x) = 3-0.5ln x-0.5x(1/x) = 3-0.5x-0.5= 2.5-0.5x
b. P '(25)= 3-0.5ln(25)-0.5 = 0.891
c. P'(25) represents the additional profit for selling a thousand candles once 25000 candles have already been sold. Correct option is A
d. P'(x)=0
2.5-0.5x=0
x = 5
5000 candles should be sold to maximize profit.
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