Profit. The financial department for the company in Problem 1 and 2 established the following cost function for producing and selling x million memory chips:
C(x) = 125 + 16x million dollars
(A) Write a profit function for producing and selling x million memory chips and indicate its domain.
(B) Complete Table 1, computing profits to the nearest million dollars.
Table 1 Profit
x (millions)
P(x) (million $)
1
−69
4
8
12
16
20
(C) Plot the points in part (B) and sketch a graph of the profit function using these points.
Problem 1
Price–demand. A company manufactures memory chips for microcomputers. Its marketing research department, using statistical techniques, collected the data shown in Table 2, where p is the wholesale price per chip at which x million chips can be sold. Using special analytical techniques (regression analysis), an analyst produced the following price–demand function to model the data:
Table 2 Price–Demand
x (millions) | p($) |
1 | 72 |
4 | 63 |
9 | 48 |
14 | 33 |
20 | 15 |
(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 chip for a demand of 7 million chips? For a demand of 11 million chips?
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 million dollars.
Table 3 Revenue
x (millions)
R(x) (million $)
1
72
4
8
12
16
20
(C) Plot the points from part (B) and sketch a graph of the revenue function using these points. Choose millions for the units on the horizontal and vertical axes.
Problem 3
Price–demand. A company manufactures memory chips for microcomputers. Its marketing research department, using statistical techniques, collected the data shown in Table 4, where p is the wholesale price per chip at which x million chips can be sold. Using special analytical techniques (regression analysis), an analyst produced the following price–demand function to model the data:
Table 4 Price–Demand
x (millions) | p($) |
1 | 72 |
4 | 63 |
9 | 48 |
14 | 33 |
20 | 15 |
(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 chip for a demand of 7 million chips? For a demand of 11 million chips?
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