Profit. The financial department for the company in Problem 1 and 2 established the following cost function for producing and selling x thousand notebook computers:
C(x) = 4,000 + 500x thousand dollars
(A) Write a profit function for producing and selling x thousand notebook computers and indicate its domain.
(B) Complete Table 1, computing profits to the nearest thousand dollars.
Table 1 Profit
x (thousands)
P(x) (thousand $)
1
−2,560
5
10
15
20
25
(C) Plot the points in part (B) and sketch a graph of the profit function using these points.
Problem 1
Price–demand. A company manufactures notebook computers. Its marketing research department, using statistical techniques, collected the data shown in Table 2, where p is the wholesale price per computer at which x thousand computers can be sold. Using special analytical techniques (regression analysis), an analyst produced the following price–demand function to model the data:
Table 2 Price–Demand
x (thousands) | p($) |
1 | 1,940 |
8 | 1,520 |
16 | 1,040 |
21 | 740 |
25 | 500 |
(A) Plot the data points in Table 2, and sketch a graph of the price–demand function in the same coordinate system.
(B) What would be the estimated price per computer for a demand of 11,000 computers? For a demand of 18,000 computers?
Problem 2
Revenue.
(A) Using the price–demand function
from Problem 3, write the company’s revenue function and indicate its domain.
(B) Complete Table 3, computing revenues to the nearest thousand dollars.
Table 3 Revenue
x (thousands)
R(x) (thousand $)
1
1,940
5
10
15
20
25
(C) Plot the points from part (B) and sketch a graph of the revenue function using these points. Choose thousands for the units on the horizontal and vertical axes.
Problem 3
Price–demand. A company manufactures notebook computers. Its marketing research department, using statistical techniques, collected the data shown in Table 4, where p is the wholesale price per computer at which x thousand computers can be sold. Using special analytical techniques (regression analysis), an analyst produced the following price–demand function to model the data:
Table 4 Price–Demand
x (thousands) | p($) |
1 | 1,940 |
8 | 1,520 |
16 | 1,040 |
21 | 740 |
25 | 500 |
(A) Plot the data points in Table 4, and sketch a graph of the price–demand function in the same coordinate system.
(B) What would be the estimated price per computer for a demand of 11,000 computers? For a demand of 18,000 computers?
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