Operations Research Answers

A departmental store has a single cashier. During the rush hours, customers arrive at the rate of 20 customers per hour. The average number of customers that can be processed by the cashier is 24 per hour.Calculate

a) Probability that the cashier is idle?b)Average number of customers in the queuing system?

A chicken sandwich has 1 serving of vegetables, 4 slices of chicken, 2 slices of cheese, and 2 slices of bread. An egg sandwich has 2 serving of vegetables, 2 servings of egg, 2 slices of cheese and 2 slices of bread. A vegetarian sandwich has 3 servings of vegetables, 2 slices of cheese, and 2 slices of bread. A total of 5 bags of chicken are available, each of which has 40 slices; 19 loaves of bread are available, each with 14 slices; 200 servings of vegetables and eggs are available, and 15 bags of cheese, each with 60 slices, are available. a)Show the answer and sensitivity report. b) Given the resources, how many of each sandwich can be produced if the goal is to maximize the number of sandwiches? c) optimal number of sandwiches? d) company wants to reduce 2 servings of vegetables, what would be the implication on the overall number of sandwiches? e) the company plans to add 5 more loaves of bread. What is your advice to the company? f) What is the shadow cost for chicken? Interpret the meaning.

Find the critical path of the following network using the EST/LSTs.

Activity Preceding Activity Duration (days)

1 - 4

2 1 7

3 1 5

4 1 6

5 2 2

6 3 3

7 5 5

8 2, 6 11

9 7, 8 7

10 3 4

11 4 3

12 9, 10, 11 4

(b). Calculate the floats of the network diagram in part (a).

(c ). The standard deviations of the activities on the critical path in part (a) are: 1, 2, 1.5, 3,

2.5 and 3 respectively. Based on these values calculate the probability of achieving a

scheduled time of 40 days for the project duration.

A catering company is to make lunch for a business meeting. It will serve salami sandwiches, and vegetarian sandwiches. A salami sandwich has 1 serving of vegetables, 4 slices of salami, 1 slice of cheese, and 2 slices of bread. A vegetarian sandwich has 3 servings of vegetables, 2 slices of cheese, and 2 slices of bread. A total of 10 bags of salami are available, each of which has 40 slices; 18 loaves of bread are available, each with 14 slices; 200 servings of vegetables are available, and 15 bags of cheese, each with 60 slices, are available. Given the resources, how many of each sandwich can be produced if the goal is to maximize the number of sandwiches? Please show all the steps of the solution

A trust fund is planning to invest up to $6000 in two types of bonds.: A and B. Bond A is safer than bond B and carries a dividend of 8% while bond B carries a dividend of 10%. Suppose that the bond’s rule state that no more than $4000 may be invested in bond B, while at least $1500 must be invested in bond A. The amount invested in bond B cannot exceed one half the amount invested in bond A. How much should be invested in each type of bond to maximize the fund’s return?

a shoe manufacturer produces midtoop and high top athletic shoes. cutting machines cut the fabric for shoes. stitching machine stitch the fabric. the cutting machines run 4 hours per day, and the stitching machines run 5 hours per day. a midtop shoe takes 3 minutes to cut and 2 minutes to stitch the profit is $13 on a midtop shoe and $16 on a hightop shoe. write the constraints

A marketing research group conducting a telephone survey must contact at least 150 wives and 120 husbands. It costs P100 to make a daytime call and (because of higher labor costs) P150 to make an evening call. On average, daytime calls reach wives 30% of the time, husbands 10% of the time, and neither of these 60% of the time, whereas evening calls reach wives 30% of the time, husbands 30% of the time, and neither of these 40% of the time. Staffing considerations mean that daytime calls must be less than or equal to half of the total calls made. How many should be interviewed at each period to minimize the cost of completing the survey?

Daily requirements of 70 g of protein, 1 g calcium, 12 mg iron, and 3000 calories are needed for a balanced diet. The following foods are available for consumption with the cost and nutrients per 100 g as shown.

Protein

(g)

Calories

Calcium

(g)

Iron

Cost

GH¢

Brown Bread

12

246

0.1

3.2

0.5

Cheese

24.9

423

0.2

0.3

2

Butter

0.1

793

0.03

0

1

Baked Beans

6

93

0.05

2.3

0.25

Spinach

3

26

0.1

2

0.25

The objective is to find a balanced diet with minimum cost.

(a) Formulate a linear programming model for this problem.

(b) Use solver to find optimal solution and sensitivity report.     

Consider the pay-off table for two players as given below:

1 2 3

Player A 1|-4 -2 6|

2| 3 0 3 |

3| 6 -3 -5 |

(i) Find the saddle point the value of the game.

(ii) Give two equivalent linear programming problems for the above problem.

1)differentiate between assignment problem and transportation problem

2) What is a slack variable