Question

Consider the following linear program:

Max 3A + 2B

1A+1B<=10

3A+ 1B<=24

1A+2B<=16

A) Run the syntax for the LINDO results.

B) Assume that the objective function coefficient for A changes from 3 to 3.8 and the objective function coefficient for B changes from 2 to 1.2. Does the optimal solution change? Show the calculation based on 100% rule on objective function.

C) Assume that the right hand side of Constraint 2 changes from 24 to 28 and Constraint 3 changes from 16 to 14.5? Will the dual price change. Show the calculation based on 100% rules for the right hand side constraints. What will be the new profit margin based on the dual price changes?

Answer #1

A) LINDO result is following:

Result:

A = 7

B = 3

Objective value = 27

B)

Run the range report on LINDO by pressing CTRL+R , while keeping the curser on LINDO model window. Range report is following:

Using 100% rule, we determine whether the sum of changes in objective coefficients as a ratio of their respective allowable change (allowable increase or decrease as applicable) is >= 100%, in which case, optimal solution would change, otherwise not.

The sum = (3.8-3)/3+(2-1.2)/1 = 1.07 or 107%

The sum is greater than 100%. Therefore, 100% rule is violated. Hence, the optimal solution changes.

C)

The sum = (28-24)/6+(16-14.5)/3 = 1.17 or 117%

100% rule is violated. Therefore, dual price may change. We need to re-run the LINDO model to get the new profit margin

New profit margin = **29**

Consider the following linear program:
Max 3A + 2B
s.t
1A + 1B 10
3A + 1B < 24
1A + 2 B < 16
A, B > 0

2. The following linear programming problem has
been solved by The Management Scientist. Use the output to answer
the questions.
LINEAR PROGRAMMING PROBLEM
MAX 25X1+30X2+15X3
S.T. 1) 4X1+5X2+8X3<1200
2) 9X1+15X2+3X3<1500
OPTIMAL SOLUTION
Objective Function Value = 4700.000
Variable Variable Reduced Cost
X1 140.000 0.000
X2 0.000 10.000
X3 80.000 0.000
Constraint Slack/Surplus Dual Price
1 0.000 1.000
2 0.000 2.333
OBJECTIVE COEFFICIENT RANGES
Variable Lower Limit Current Value Upper Limit
X1 19.286 25.000 45.000
X2 No Lower Limit 30.000 40.000...

Consider this problem and answer the following questions.
Maximize Z = 2x1 + 3x2
s.t.
x1 + 2x2 <= 30
x1 + x2 <=
20
x1,
x2 >= 0
Solve the problem graphically in a free hand manner and
identify all the CPFs.
Use hand calculation to solve the problem by the simplex method
in algebraic form
Additional:
What can you say about the solution if the RHS of the second
constraint was 16? (i. e....

Answer Questions 2 and 3 based on the following LP
problem.
Let P1 = number of Product 1 to be
produced
P2 =
number of Product 2 to be produced
P3 =
number of Product 3 to be produced
Maximize 100P1 + 120P2 +
90P3 Total
profit
Subject to
8P1 + 12P2 + 10P3 ≤
7280 Production budget
constraint
4P1 + 3P2 + 2P3 ≤ 1920 Labor
hours constraint
P1
> 200 Minimum
quantity needed...

MATHEMATICS
1. The measure of location which is the most likely to
be
influenced by extreme values in the data set is the a. range
b.
median c. mode d. mean
2. If two events are independent, then a. they must be
mutually
exclusive b. the sum of their probabilities must be equal to one
c.
their intersection must be zero d. None of these alternatives
is
correct. any value between 0 to 1
3. Two events, A and B,...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 11 minutes ago

asked 11 minutes ago

asked 14 minutes ago

asked 30 minutes ago

asked 39 minutes ago

asked 45 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago