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QUESTION 1

Rift Valley University, Burayu Campus
Department of Business Management
For First Year MBA students, 2021/22 Academic year

QUANTITATIVE ANALYSIS FOR MANAGEMENT DECISIONS (MBA 641)
Group Assignment 30%
Instruction: Answer the following questions according to the given instruction (3 points each)

  1. A company is involved in the production of two items (X and Y). The resources need to produce X and Y are twofold, namely machine time for automatic processing and craftsman time for hand finishing. The table below gives the number of minutes required for each item:

Machine time Craftsman time
Item X 13 20
Item Y 19 29
The company has 40 hours of machine time available in the next working week but only 35 hours of craftsman time. Machine time is priced at £10 per hour worked and craftsman time is costed at £2 per hour worked. Both machine and craftsman idle times incur no costs. The revenue received for each item produced (all production is sold) is £20 for X and £30 for Y. The company has a specific contract to produce 10 items of X per week for a particular customer.
Formulate the problem of deciding how much to produce per week as a linear program.

  1. Answer the questions related to the model below:

max. 3 x1 + 2 x2
st 2 x1 + 2 x2 = 5
x1 + x2 = 4
x1 + 2 x2 = 4
x1, x2 = 0

  1. Use the graphical solution technique to find the optimal solution to the model.
  2. Use the simplex algorithm to find the optimal solution to the model.
  3. For which objective function coefficient value ranges of x1 and x2 do the solution remain optimal?
  4. Find the dual of the model.
  1. Use the revised simplex algorithm manually to solve the following problem. min 5x1 + 2x2 + 4x3

s.t. 3x1 + x2 + 2x3 = 4 6x1 + 3x2 + 5x3 = 10 x1, x2, x3 = 0

  1. Addis Ababa Police Station employs 30 police officers. Each officer works 5 days per week. The crime rate fluctuates with the day of the week, so the number of the police officers required each day depends on which day of the week it is: Monday, 18; Tuesday, 24; Wednesday, 25; Thursday, 16; Friday, 21; Saturday, 28; Sunday, 18. The Police Station wants to schedule police officers to minimize the number whose days off are not consecutive. Formulate an LP that will accomplish this goal.
  1. A shoe company forecasts the following demands during the next three months: 200, 260, 240. It costs

$7 to produce a pair of shoes with regular time labor (RT) and $11 with overtime labor (OT). During each month regular production is limited to 200 pairs of shoes, and overtime production is limited to 100 pairs. It costs $1 per month to hold a pair of shoes in inventory. Formulate a balanced transportation problem to minimize the total cost of meeting the next three months of demand on time (Do not try to solve it!).

  1. Recall that the optimal solution for the Power problem was z=$1,020 and the optimal tableau was:
UI/vj City 1
6
City 2
6
City 3
10
City 4
2
Supply
8 6 10 9
Plant 1 0 10 25 35
9 12 13 7
Plant 2 3 45 5 50
14 9 16 5
Plant 3 3 10 30 40
Demand 45 20 30 30
  1. For what range of values of the cost of shipping 1 million kWh of electricity from plant 3 to city 3 will the current basis remain optimal?
  2. Suppose we increase both s3 and d3 by 3. Find the new value of the cost and new values of the decision variables.
  1. Nicole Kidman, Jennifer Lopez, Catherine Zeta-Jones, and Cameron Diaz are marooned on a desert island with Brad Pitt, Antonio Banderas, Robin Williams, and Tom Cruise. The “compatibility measures” in the table given below indicate how much happiness each couple would experience if they spent all their time together. Determine the partner for each person.
NK JL CZJ CD
BP 7 5 8 2
AB 7 8 9 4
RW 3 5 7 9
TC 5 7 6 9
  1. A company is taking bids on four construction jobs. Three people have placed bids on the jobs. Their bids (in thousands of dollars) are given in the table (a * indicates that the person did not bid on the given job). Person 1 can do only one job, but persons 2 and 3 can each do as many as two jobs.
  1. built an assignment table to determine the minimum cost assignment of persons to jobs,
  2. use the Hungarian method to find the assignment of persons to jobs.
Job
Person 1 2 3 4
1 50 46 42 40
2 51 48 44 *
3 * 47 45 45
  1. Consider the following transportation table for a minimization problem.

1 2 3 4 Supply 1
2
3
Demand

100 60
60

3 4 3 3
6 5 9 4
3 2 1 2

70
90
40 20

  1. A basic feasible solution for the given transportation is given as BV: {x11, x13, x21, x24, x32, x33}. Find the values of the basic variables. Prove that this solution is not optimal.
  2. Find the optimal solution using the transportation simplex method starting from the basic feasible solution given in part a.
  3. Find the range of values of the c24 (the cost related to x24i) for which the current basis remains optimal.
  1. Critically and objectively explain by giving examples the role of game theory in managerial decision-making.

NB. Date of submission 15/04/2022… submitted in hard copy only
Adapted and set by Getachew Gobena (Asst. Prof.)
QUESTION1,
Answer to Question #56576 – Math – Other
A company is involved in the production of two items (X and Y). The resources need to produce X and Y are twofold, namely machine time for automatic processing and craftsman time for hand finishing. The table below gives the number of minutes required for each item:
Machine time Craftsman time
Item X 13 20
Item Y 19 29
The company has 40 hours of machine time available in the next working week but only 35 hours of craftsman time. Machine time is costed at £10 per hour worked and craftsman time is costed at £2 per hour worked. Both machine and craftsman idle times incur no costs. The revenue received for each item produced (all production is sold) is £20 for X and £30 for Y. The company has a specific contract to produce 10 items of X per week for a particular customer. Formulate the problem of deciding how much to produce per week as a linear program hence make the decision.
Solution
Let ?? be the number of items of ??, ?? be the number of items of ??.
Then the LP is
maximize
20?? + 30?? – 10(??????h?????? ???????? ????????????) – 2(?????????????????? ???????? ????????????)
subject to:
13?? + 19?? = 40(60) ??????h?????? ????????
20?? + 29?? = 35(60) ?????????????????? ????????
?? = 10 ????????????????
??, ?? = 0
so that the objective function becomes
maximize
20?? + 30?? – 10(13?? + 19??) – 2(20?? + 29??)
60 60
i.e. maximize
17.1667?? + 25.8667??
subject to:
13?? + 19?? = 2400
20?? + 29?? = 2100
?? = 10
??, ?? = 0
It is plain from the diagram below that the maximum occurs at the intersection of ?? = 10 and
20?? + 29?? = 2100.
Solving simultaneously, rather than by reading values off the graph, we have that ?? = 10 and ?? = 65.52
with the value of the objective function being £1866.5.

QUESTION 2

Question 1. Which sequence can serve as the best template for modeling the E3 ubiquitin-protein ligase structure? Give a reason for the same. Use the parameters like score, identity, similarity, query • coverage, E-value, etc. to make the choice.
Question 2. Show the alignment of the chosen template with your query protein. Is there any region of the query that is not being covered by the template? If yes, mention the residue numbers. Use the graphical summary on the results page to check if any other sequence can serve as a template for the uncovered region or not

QUESTION 3

12
M1L1 Fluids, Density, and Pressure
Name: Section:
Date:
The assessment quantity of helium gas at 0°C used to inflate balloons has a volume of 4.0 m3 and a volume of 0.712 kg. The gas is at atmospheric pressure. What is its density?

  1. Rewrite the equation= m / V to solve for the a) mass and b) volume.

Learning Module on Fluid Mechanics 13

  1. A rectangular brass plate is 3.15 in length, 6.0 cm wide, and 0.015 m thick.
    1. Calculate the volume of the plate in cubic centimeters.
    2. Calculate the plate’s mass in grams and kilograms.
  1. What pressure will Vangie feel if she is submerged under saltwater with a depth of 235 cm? Vangie weighs 78 kilograms.

Learning Module on Fluid Mechanics
14

  1. A mattress of a waterbed is 2.0 m long, 25 in wide, and 30 cm deep. Find the following:
    1. the mass of the water in the mattress
    2. the pressure exerted by the waterbed on the floor while the bed rests in its normal position.
    3. the pressure of the waterbed exerted on the floor if the bed is supported by four legs and each leg has a radius of 3.0 cm.

Learning Module on Fluid Mechanics

Attachments:

QUESTION 4

Leo wants to paint a mural that covers a wall with an area of 300 square feet. The height of the wall is 1/3 of its length. What are the length and the height of the wall?

 QUESTION 5

Basic body color for horses is influenced by several genes, one of which has several different alleles. Two of this alleles-the chestnut (dark brown) allele and a diluting (pale cream) allele (often incorrectly called ‘albino’)-display incomplete dominance. A horse heterozygous for these two alleles is a palomino (golden body colorbody-color with flaxen mane and tail). Is it possible to produce a herd of pure-breeding palomino horses? Why or why not? Work the Punnett’s square for mating a palomino to a palomino and predict the phenotypic ratio among their offspring.

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