Reference no: EM13707120
Question 1:
For the following tableau:
a. Label the rows with the variable names in the current solution.
b. State the current solutions variable name and value and objective function value
c. Perform one simplex method iteration showin p all values for ratios and row o erations for row 0 and pivot row.
Basic
|
Z
1
|
x1
0
|
x2 -2/3
|
x3
5/6
|
x4
|
x5
0
|
x6
0
|
r.h.s.
20 tig.
4
|
|
0
|
1
|
213
|
1/6
|
0
|
0
|
0
|
2
|
|
0
|
0
|
1 1/3
|
- 1/6
|
1
|
0
|
0
|
2
|
|
0
|
0
|
1 2/3
|
1/6
|
0
|
1
|
0
|
2
|
|
0
|
0
|
1
|
0
|
0
|
0
|
1
|
|
d. What variables are in the new solution?
e. Is the solution optimal and why?
Question 2:
TOYCO assembles three types of toys-trains, trucks, and cars-using three operations. The daily limits on the available times for the three operations are 430,460, and 420 minutes, respec¬tively, and the revenues per unit of toy train. tructand car are $3, 52, and $5.respectively.The as¬sembly times per train at the three operations are 1, 3, and 1 minutes, respectively. The corresponding times per train and per car are (2,0,4) and (1,2,0) minutes (a zero time indicates that the operation is not used).
Letting x1, x2, and x3 represent the daily number of units assembled of trains, trucks, and cars, respectively, the associated LP model is given as:
Maximize z = 3x1 + 2x2 + 5x3
subject to
x1 + 2x2 + x3 ≤ 430 (Operation 1)
3x1 + 2x3 ≤ 460 (Operation 2)
x1 + 4x2 ≤ 420 (Operation 3)
x1, x2, x3 ≥ 0
Using x4. x5, and x6 as the slack variables for the constraints of operations 1,2, and 3, respectively, the optimum tableau is
Basic
|
X1
|
X2
|
X3
|
X4
|
X5
|
X6
|
Solution
|
z
|
4
|
0
|
0
|
1
|
2
|
0
|
1350
|
x2
|
|
1
|
0
|
1/2
|
-1/4
|
0
|
100
|
-1/4
|
X3
|
3/2
|
0
|
1
|
0
|
1/2
|
0
|
230
|
X6
|
2
|
0
|
0
|
-2
|
1
|
1
|
20
|
a. What is the production plan? Number of trains =
Number of trucks =
Number of cars =
b. What are the shadow prices for one more minute of time at each operation?
c. If one more unit of time in operation 2 were available, what would be the new value of the objective function?
d. what is the basis matrix of the current solution?
e. Verify the current solution by calculating x = B-1b and labeling the x variables.
F. FOR EXTRA CREDIT calculate the new solution (x's and z with 461 minutes available at operation 2).
How many chloride ion lattice points are in the unit cell
: Question- A unit cell of sodium chloride (face-centered cubic) was chosen so that the face-centered cube was formed from sodium ions. A certain number of sodium ion lattice points and a certain number of chloride ion lattice points are required. H..
|
Review the it online training specification description
: Review the IT Online Training Specification description - Develop an application class model that includes entity classes, user interface classes, boundary, and controller classes. Review the use cases to make certain that the application class mod..
|
Explain why the general trend exists for elements
: Question- Explain why the general trend exists for elements getting smaller as you move across a period on the periodic table.
|
Changing the role of technology at work place
: Directions: Now that you have considered your audience and purpose (from the LP1 assignment) for your final proposal paper, this week you are going to narrow down a specific topic and write your ideas and main points in a formal outline format. Ou..
|
What is the production plan
: Label the rows with the variable names in the current solution and State the current solutions variable name and value and objective function value and perform one simplex method iteration showin p all values for ratios and row o erations for row 0 a..
|
Calculate the force constant k
: A) Coil springs are widely used in industry. Those used in scientific instruments must be manufactured to exhibit consistent performance. One important property of a spring is its force constant. As the quality control manager of a coil spring man..
|
One big lie can destroy thousands of lives
: Read Case Study 1, "Bernie Madoff: How "One Big Lie" Can Destroy Thousands of Lives," on pages 258-264. Summarize the overall viewpoint of the author, and discuss the major issues presented in the case. Review the "Questions for Thought." Answer t..
|
Political risk is inherent to investing in developing nation
: Political Risk is inherent to investing in developing nations and emerging markets. Please read this article from the Central Bank of Peru (Rossini, Quispe and Rodríguez (2011) that discusses a policy called 'sterilization'. It is a monetary polic..
|
Three-quarters of its revenue from overseas markets
: Coca-Cola, a well-known U.S. multinational company, derives about three-quarters of its revenue from overseas markets. It is thus highly likely that the company is exposed to currency risks. Investigate the company's exchange risk management polic..
|