Log in
HomeStudy Guides420,000CA160,000

MATH 340 Midterm: MATH 340 2011 Winter Test 1

46 views5 pages
turquoisegnu128
9 Jan 2019
School
UBC
Department
Mathematics
Course
MATH 340
Professor
All

For unlimited access to Study Guides, a Grade+ subscription is required.

Document Summary

You must show your work and explain your answers. Total marks: 100 names of theorems used as appropriate. Time: 3 hours: [12 marks, [10pts] solve the following linear programming problem, using our standard two phase method and using anstee"s rule. 2x2 x3 5 x1, x2, x3 0: [2 marks] give two optimal solutions, [12 marks] consider the following linear program: Determine an optimal dual solution (without pivoting), stating which theorems you have used: [2 marks] consider replacing the rst inequality of the primal by 2x1 + 3x2 + x3 10. 3 = 3 and the optimal dual solution determined in c) 2 = 2, x : [8 marks] given a, b, c, current basis (and b 1 for your computational ease), use our revised. The current basis is {x5, x2, x4}. x1. 1 x1 x2 x3 x4 x5 x6 x7.

Get access

Grade+20% off
$8 USD/m$10 USD/m
Billed $96 USD annually
Grade+
Homework Help
Study Guides
Textbook Solutions
Class Notes
Textbook Notes
Booster Class
40 Verified Answers

Related textbook solutions

Calculus
4 Edition,
Rogawski
ISBN: 9781319050733
Single Variable Calculus: Early Transcendentals
4th Edition, 2018
Stewart
ISBN: 9781337687805
CALCULUS:EARLY TRANSCENDENTALS
4 Edition,
Rogawski
ISBN: 9781319050740

Related Documents

MATH 340 Lecture Notes - Lecture 4: Slack Variable, Linear Programming, Linear Algebra
roseimpala891
MATH 340 Lecture Notes - Lecture 6: Linear Programming
roseimpala891
MATH 340 Lecture Notes - Lecture 18: Linear Programming, Feasible Region
roseimpala891

Related Questions

Linear Programming: The Dual Simplex Method

Problem 18

Do a, c,d. Solve part (c) only. For part (a) and (d), just write down the initial table

Show transcribed image text

Q18. A size 6 dress in Country C is size 52 in Country D. A function that converts dress sizes in Country C to those in Country D is f(x) = 2(x + 20). Find a formula for the inverse of the function described.
a. f -1(x) = (x - 20)/2
b. f -1(x) = x - 20
c. f -1(x) = (x/2) - 20
d. f -1(x) = (x/2) + 20

Q19. If f(x) = 4x and g(x) = 12, find the point of intersection of the graphs of f and g by solving f(x) = g(x). Give an exact answer.
a. (log 4 12, 12)
b. (log 4 12, 4)
c. (log 4 12, 0)
d. (12, 12)

Q20. Find functions f and g so that f ∘ g = H(x) = (5 - 2x3)2.
a. f(x) = 5 - 2x3 ; g(x) = x2
b. f(x) = (5 - 2x)3 ; g(x) = x2
c. f(x) = x2 ; g(x) = 5 - 2x3
d. f(x) = x3 ; g(x) = (5 - 2x)2

Q29. Solve the system of equations using Cramer's Rule if it is applicable.


a. x = 9, y = 2, z = 5; (9, 2, 5)
b. x = 8, y = 4, z = 5; (8, 4, 5)
c. x = 4, y = 5, z = 4; (4, 5, 4)
d. x = 8, y = -4, z = -5; (8, -4, -5)

Q30. Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent.


a. x = 2, y = 3, z = -7; (2, 3, -7)
b. x = 1, y = 3, z = -4; (1, 3, -4)
c. x = 5, y = 13/2, z = -3; (5, 13/2, -3)
d. x = 1, y = -3, z = -16; (1, -3, -16)

Q33. Write the partial fraction decomposition of the rational expression (4x3 + 4x2)/(x2 + 5)2.
a. (4x - 4)/(x2 + 5) + (-20x + 20)/(x2 + 5)2
b. (4x + 4)/(x2 + 5) + (-20x - 20)/(x2 + 5)2
c. (4x + 4)/(x2 + 5) + (20x - 20)/(x2 + 5)2
d. (4x + 4)/(x2 + 5) + (20x + 20)/(x2 + 5)2

Q34. Solve the linear programming problem. Minimize z = 11x + 6y + 7 subject to: x = 0, y = 0, x + y = 1.
a. minimum: 7
b. minimum: 18
c. minimum: 24
d. minimum: 13

Q35. Solve the system of equations by elimination.


a. x = 10, y = 0; (10, 0)
b. x = 10, y = 10; (10, 10)
c. x = 0, y = 10; (0, 10)
d. x = 0, y = 0; (0, 0)

Q36. Perform the row operations on the given augmented matrix.


a.
b.
c.
d.

Q37. Solve the system of equations using Cramer's Rule if it is applicable.


a. x = -4, y = 3; (-4, 3)
b. x = -3, y = -4; (-3, -4)
c. x = 4, y = 3; (4, 3)
d. x = 3, y = 4; (3, 4)

Q38. Write the partial fraction decomposition of the rational expression x/(x2 - 9x + 20).
a. -4/(x - 4) + 5/(x - 5)
b. -5/(x - 4) + 4/(x - 5)
c. 4/(x - 4) + -5/(x - 5)
d. -4/(x - 4) + -5/(x - 5)

Q39. Solve the system of equations.


a. x = -4, y = 4, z = -3; (-4, 4, -3)
b. x = -3, y = 4, z = -4; (-3, 4, -4)
c. x = -4, y = -3, z = 4; (-4, -3, 4)
d. inconsistent

Q40. Find the value of the determinant.


a. 224
b. 24
c. -72
d. 72

Show transcribed image text

I need help with these as soon as possible Please. Thank You!!

Q15. In 1990, the population of a country was estimated at 4 million. For any subsequent year the population, P(t) (in millions), can be modeled by the equation P(t) = 240/(5 + 54.99e-0.0208t), where t is the number of years since 1990. Estimate the year when the population will be 21 million.
a. approximately the year 2093
b. approximately the year 2041
c. approximately the year 2088
d. approximately the year 2016

Q18. A size 6 dress in Country C is size 52 in Country D. A function that converts dress sizes in Country C to those in Country D is f(x) = 2(x + 20). Find a formula for the inverse of the function described.
a. f -1(x) = (x - 20)/2
b. f -1(x) = x - 20
c. f -1(x) = (x/2) - 20
d. f -1(x) = (x/2) + 20

Q19. If f(x) = 4x and g(x) = 12, find the point of intersection of the graphs of f and g by solving f(x) = g(x). Give an exact answer.
a. (log 4 12, 12)
b. (log 4 12, 4)
c. (log 4 12, 0)
d. (12, 12)

Q20. Find functions f and g so that f ∘ g = H(x) = (5 - 2x3)2.
a. f(x) = 5 - 2x3 ; g(x) = x2
b. f(x) = (5 - 2x)3 ; g(x) = x2
c. f(x) = x2 ; g(x) = 5 - 2x3
d. f(x) = x3 ; g(x) = (5 - 2x)2

Q29. Solve the system of equations using Cramer's Rule if it is applicable.


a. x = 9, y = 2, z = 5; (9, 2, 5)
b. x = 8, y = 4, z = 5; (8, 4, 5)
c. x = 4, y = 5, z = 4; (4, 5, 4)
d. x = 8, y = -4, z = -5; (8, -4, -5)

Q30. Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent.


a. x = 2, y = 3, z = -7; (2, 3, -7)
b. x = 1, y = 3, z = -4; (1, 3, -4)
c. x = 5, y = 13/2, z = -3; (5, 13/2, -3)
d. x = 1, y = -3, z = -16; (1, -3, -16)

Q33. Write the partial fraction decomposition of the rational expression (4x3 + 4x2)/(x2 + 5)2.
a. (4x - 4)/(x2 + 5) + (-20x + 20)/(x2 + 5)2
b. (4x + 4)/(x2 + 5) + (-20x - 20)/(x2 + 5)2
c. (4x + 4)/(x2 + 5) + (20x - 20)/(x2 + 5)2
d. (4x + 4)/(x2 + 5) + (20x + 20)/(x2 + 5)2

Q34. Solve the linear programming problem. Minimize z = 11x + 6y + 7 subject to: x = 0, y = 0, x + y = 1.
a. minimum: 7
b. minimum: 18
c. minimum: 24
d. minimum: 13

Q35. Solve the system of equations by elimination.


a. x = 10, y = 0; (10, 0)
b. x = 10, y = 10; (10, 10)
c. x = 0, y = 10; (0, 10)
d. x = 0, y = 0; (0, 0)

Q36. Perform the row operations on the given augmented matrix.


a.
b.
c.
d.

Q37. Solve the system of equations using Cramer's Rule if it is applicable.


a. x = -4, y = 3; (-4, 3)
b. x = -3, y = -4; (-3, -4)
c. x = 4, y = 3; (4, 3)
d. x = 3, y = 4; (3, 4)

Q38. Write the partial fraction decomposition of the rational expression x/(x2 - 9x + 20).
a. -4/(x - 4) + 5/(x - 5)
b. -5/(x - 4) + 4/(x - 5)
c. 4/(x - 4) + -5/(x - 5)
d. -4/(x - 4) + -5/(x - 5)

Q39. Solve the system of equations.


a. x = -4, y = 4, z = -3; (-4, 4, -3)
b. x = -3, y = 4, z = -4; (-3, 4, -4)
c. x = -4, y = -3, z = 4; (-4, -3, 4)
d. inconsistent

Q40. Find the value of the determinant.


a. 224
b. 24
c. -72
d. 72

Show transcribed image text