Revenue Function for Electric Cars Bell Motors manufactures two models of electric cars. The demand equations giving the relationship between the unit price, p and q, and the number of cars demanded per year, x and y, of Models S1 and S p - 60,000 - 4x - 2y and a - 50,000 - 2x - 4y respectively. (a) What is the total yearly revenue function R(x, y)? R(x, y) = (b) What is the domain of R? O The set of all x and y satisfying the system of inequalities 4x - 2y s 50,000, 2x - 4y s 60,000, x 2 0, y 2 0. O The set of all x and y satisfying the system of inequalities 4x - 2y s 60,000, 2x - 4y s 50,000, x 2 0, y 20. O The set of all x and y satisfying the system of inequalities 4x + 2y s 60,000, 2x + 4y 2 50,000, x 2 0, y 2 0. O The set of all x and y satisfying the system of inequalities 4x + 2y s 50,000, 2x + 4y s 60,000, x 2 0, y 2 0. O The set of all x and y satisfying the system of inequalities 4x + 2y s 60,000, 2x + 4y s 50,000, x 2 0, y 2 0. Sketch the domain R. y y y 25 000 30 000 30 000 25 000 25 000 25 000 20 000 20000- domain of R 20000 20 000- 15 000 15 000 domain of R 15 000 15 000- 10 000 10 000 10000- 10 000 5000 5000 5000 5000 domain of R domain of R 5000 1000015 000 20000 25 000 30 000 5000 10000 15000 20000 25 000 5000 10000 15000 20000 25 000 5000 10000 15 000 20000 25 000 30 000 (c) Is the point (4,000, 5,000) in the domain of R? Interpret your result. Hint: Show that x = 4,000 and y = 5,000 satisfy the system of inequalities obtained in part (b). When we substitute x - 4,000 and y - 5,000 into each of the inequalities, al vv of the inequalities are satisfied. The point (x, v) - (4,000, 5,000) I5 vv in the domain of R sketched in part (b). (d) What is the total revenue (in millions of dollars) realized by Bell Motors if it sells 4,000 Model Sis and 5,000 Model S2s?
Revenue Function for Electric Cars Bell Motors manufactures two models of electric cars. The demand equations giving the relationship between the unit price, p and q, and the number of cars demanded per year, x and y, of Models S1 and S p - 60,000 - 4x - 2y and a - 50,000 - 2x - 4y respectively. (a) What is the total yearly revenue function R(x, y)? R(x, y) = (b) What is the domain of R? O The set of all x and y satisfying the system of inequalities 4x - 2y s 50,000, 2x - 4y s 60,000, x 2 0, y 2 0. O The set of all x and y satisfying the system of inequalities 4x - 2y s 60,000, 2x - 4y s 50,000, x 2 0, y 20. O The set of all x and y satisfying the system of inequalities 4x + 2y s 60,000, 2x + 4y 2 50,000, x 2 0, y 2 0. O The set of all x and y satisfying the system of inequalities 4x + 2y s 50,000, 2x + 4y s 60,000, x 2 0, y 2 0. O The set of all x and y satisfying the system of inequalities 4x + 2y s 60,000, 2x + 4y s 50,000, x 2 0, y 2 0. Sketch the domain R. y y y 25 000 30 000 30 000 25 000 25 000 25 000 20 000 20000- domain of R 20000 20 000- 15 000 15 000 domain of R 15 000 15 000- 10 000 10 000 10000- 10 000 5000 5000 5000 5000 domain of R domain of R 5000 1000015 000 20000 25 000 30 000 5000 10000 15000 20000 25 000 5000 10000 15000 20000 25 000 5000 10000 15 000 20000 25 000 30 000 (c) Is the point (4,000, 5,000) in the domain of R? Interpret your result. Hint: Show that x = 4,000 and y = 5,000 satisfy the system of inequalities obtained in part (b). When we substitute x - 4,000 and y - 5,000 into each of the inequalities, al vv of the inequalities are satisfied. The point (x, v) - (4,000, 5,000) I5 vv in the domain of R sketched in part (b). (d) What is the total revenue (in millions of dollars) realized by Bell Motors if it sells 4,000 Model Sis and 5,000 Model S2s?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Transcribed Image Text:Revenue Function for Electric Cars
Bell Motors manufactures two models of electric cars. The demand equations giving the relationship between the unit price, p and g, and the number of cars demanded per year, x and y, of Models S1 and S2 a
p = 60,000 - 4x - 2y
and
g = 50,000 - 2x - 4y
respectively.
(a) What is the total yearly revenue function R(x, y)?
R(x, y) =
(b) What is the domain of R?
O The set of all x and y satisfying the system of inequalities 4x - 2y s 50,000, 2x - 4y s 60,000, x 2 0, y 2 0.
O The set of all x and y satisfying the system of inequalities 4x - 2y s 60,000, 2x - 4y s 50,000, x 2 0, y 2 0.
O The set of all x and y satisfying the system of inequalities 4x + 2y s 60,000, 2x + 4y 2 50,000, x 2 0, y 2 0.
O The set of all x and y satisfying the system of inequalities 4x + 2y s 50,000, 2x + 4y s 60,000, x 2 0, y 2 0.
O The set of all x and y satisfying the system of inequalities 4x + 2y s 60,000, 2x + 4y < 50,000, x 2 0, y 2 0.
Sketch the domain R.
y
y
25 000
30 000
30 000
25 000
25 000
25 000-
20 000
20 000-
domain of R
20 000
20 000
15 000
15 000
domain of R
15 000
15 000
10 000
10 000
10 000
10 000
5000
5000
5000
5000
domain of R
domain of R
5000 10000 15 000 20 000 25 000 30 000
5000
10000 15 000 20 000 25 000
5000 10000 15 000 20 000 25 000
5000 1000015 000 20000 25 000 30 000
(c) Is the point (4,000, 5,000) in the domain of R? Interpret your result. Hint: Show that x = 4,000 and y = 5,000 satisfy the system of inequalities obtained in part (b).
When we substitute x = 4,000 and y = 5,000 into each of the inequalities, all
of the inequalities are satisfied. The point (x, y) = (4,000, 5,000) is
in the domain of R sketched in part (b).
(d) What is the total revenue (in millions of dollars) realized by Bell Motors if it sells 4,000 Model Sis and 5,000 Model S2s?
million
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