Quantitative Methods - section 6.pdf in business administration

Quantitative methods in business is very important course

1. Quantitative Methods for
Business
Section6
Chapter (7) : Linear Programming

2. DeterminetheStepsofDevelopingaLinearProgramming
(LP)Model?
Formulation.
Solution.
InterpretationandSensitivityAnalysis.

3. WhatarethePropertiesoflinearprogrammingmodels?
Seektominimizeormaximize.
Include“constraints”orlimitations.
Theremustbealternativesavailable.
Allequationsarelinear.

4. True or False
Linearprogrammingmodelsseektominimizeormaximize.
True
Linearprogrammingmodelsdonotincludeconstraintsor
limitations. False
Alternativesmustnotbeavailableinlinearprogramming
models. False
Allequationsinlinearprogrammingmodelsarelinear.
True

5. Multiple Choice
1.The maximization or minimization of a quantity is the
A. goal of management science.
B. decision for decision analysis.
C. constraint of operations
research.
D. objective of linear programming
Answer: D

6. Multiple Choice
2.Decision variables………………
A. tell how much or how many of something to produce,
invest, purchase, hire,
etc.
B. represent the values of the constraints.
C. measure the objective function.
D. must exist for each constraint.
Answer: A

7. 3.A solution that satisfies all the constraints of a linear
programming problem except the nonnegativity constraints is
called
A. optimal.
B. feasible.
C. infeasible.
D. semi-feasible
Answer: C
Multiple Choice

8. 4.All linear programming problems have all of the
following properties EXCEPT
A. a linear objective function that is to be maximized or
minimized.
B. a set of linear constraints.
C. alternative optimal solutions.
D. variables that are all restricted to nonnegative value
Answer: C
Multiple Choice

9. Multiple Choice
5.If there is a maximum of 4,000 hours of labor available per
month and 300 ping-pong balls (x1) or 125 wiffle balls (x2)
can be produced per hour of labor, which of the following
constraints reflects this situation?
A. 300x1 + 125x2 > 4,000
B. 300x1 + 125x2 < 4,000
C. 425(x1 + x2) < 4,000
D. 300x1 + 125x2 = 4,000
Answer: B

10. Multiple Choice
6.Which of the following statements is NOT true?
A. A feasible solution satisfies all constraints.
B. An optimal solution satisfies all constraints.
C. An infeasible solution violates all constraints.
D. A feasible solution point does not have to lie on the
boundary of the feasible region.
Answer: C

11. Multiple Choice
7.A widely used mathematical programming technique
designed to help managers and decision making relative to
resource allocation is called:
A.Linear programming
B.Computer programming
C.Constraint programming
D.Goal programming
Answer: A

12. Multiple Choice
8.Consider the following linear programming problem:
Maximize 12X + 10Y
Subject to:
4X + 3Y ≤ 480
2X + 3Y ≤ 360
all variables ≥ 0
The maximum possible value for the objective function is
A.480
B.1560
C.1520
D.360
Answer : 1520

13. Multiple Choice
10.Consider the following linear programming problem:
Maximize4X + 10Y
Subject to: 3X + 4Y ≤ 480
4X + 2Y ≤ 360
all variables ≥ 0
The feasible corner points are (48,84), (0,120), (0,0), (90,0).
What is the maximum possible value for the objective function?
A.1200
B. 1032
C.360
D.1600
Answer: A

14. FromthefollowingFormulations:
Maximize$7X+$5Y
3X+4Y=2400
2X+Y=1000
Y=450
X=100
max (z) =……………………………………………………………….
a.3000 b-2950 c-4040 d-5100
*The quantity produced of x = …………………………………………
a-450 b-360 c-200 d-320
*The quantity produced of y =
a-360 b-100 c-320 d-200

15. 3X+4Y=2400
X=0 Y=600
(0,600)
3X+4Y=2400
X=800Y=0
(800,0)
2X+Y=1000
X=0 Y=1000
(0,1000)
2X+Y=1000
X=500 Y=0
(500,0)
Answer

16. L
K
M
N
12
3
4
5

17. 1
(500,0)
2(100,0)
3L & K
3 X + 4 Y = 2400
2 X + Y = 1000
6 X + 8 Y = 4800
6 X + 3 Y = 3000
(320,360)
4K & M
3 X + 4 Y = 2400
Y= 450
(200,450)
M & N
Y= 450
X=100
(100,450)
5

18. 1(500,0)
2(100,0)
3(320,360)
(200,450)
(100,450)
4
5
Maximize$7X+$5Y
3500 $
700 $
4040 $
3650 $
2950 $

19. max (z) =
……………………………………………………………….
a.3000 b-2950 c-4040 d-5100
*The quantity produced of x =
…………………………………………
a-450 b-360 c-200 d-320
*The quantity produced of y =
a-360 b-100 c-320 d-200

20. The Shader Electronics Company produces two products: (1) the Shader x-pod,
a portable music player, and (2) the Shader BlueBerry, an internet-connected
colourtelephone. The production process for each product is similar in that both
require a certain number of hours of electronic work and a certain number of
labour-hours in the assembly department. Each x-pod takes 4 hours of electronic
work and 2 hours in the assembly shop. Each BlueBerryrequires 3 hours in
electronics and 1 hour in assembly. During the current production period, 240
hours of electronic time are available, and 100 hours of assembly department
time are available. Each x-pod sold yields a profit of $7; each BlueBerry
produced can be sold for a $5 profit. Shader’sproblemis to determine the best
possible combination of x-pods

21. Department x1 x2 Available hours
Electronic 4 3 240
Assembly 2 1 100
Profit per unit7 5
Step 1: Define the decision variables
x1 = number of x-pods to be produced x2 = number of BlueBerrysto be
produced
Step 2: Identify the objective function Maximize profit or z= 7x1+ 5x 2
Step 3: Identify the constraints 4x1+ 3x2 ≤ 240 (Electronic department
resource constraint) 2x1+ 1x2 ≤ 100 (Assembly department resource
constraint) x1and x2≥ 0 (Non-negativity)

22. 1.What would the objective function?
A: maximize profit =7X1+ 5X2
B: minimize cost =X1+X2
C: maximize =X1+12X2
D: none of the above
Answer: A
2. Which of the following would be constraints in the problem?
A: 4X1+3X2≤240 &2X1+1X2 ≤100
B: X1,X2 ≤ 0
C: X1=7
D: X2= 5
Answer : A