Operations Research Answers

Food For U Sdn Bhd., a catering company is to make breakfast for a business meeting. It will serve chicken sandwiches, egg sandwiches, and vegetarian sandwiches. 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) Formulate linear programming model based on the above problem by using Microsoft Excel. Show the answer and sensitivity report. (9 marks)

b) Given the resources, how many of each sandwich can be produced if the goal is to maximize the number of sandwiches? (3 marks)

10. The optimal solution of a maximization type LPP is given in the following table:

C sj

′ 6 4 0 0 0 

Solution

CB 

Basic Variables 

1

x 2

x 3

x 4

x 5

x

0 3

x 0 5/3 1 − 3/2 0 14 

0 5

x 0 − 3/1 0 1/3 1 5 

6 1

x 1 2/3 0 1/3 0 8 

Cj − Z j

0 0 0 − 2 0 Z = 48

 (i) Find the alternative optimal basic feasible solution. 

 (ii) Find an alternative optimal non-basic feasible solution.

9. Solve the ILLP given below by graphical method: (10)

Maximum 95 1 100 2 Z = x + x

Subject to the Constraints

5x1 + 2x2 ≤ 20

x1 ≥ 3

5 x2 ≤

1 2

x x are non-negative integers.

8(b) A trading company buys and sells 10,000 bottles of pain-balm every year. The

company’s cost of placing an order of pain-balm is Rs. 100. The holding cost per

bottle on inventory is Rs. 0.3. (5)

(i) Determine the optimum order quantity and inventory cycle time for the pain-balm,

bottles.

(ii) How many orders should be placed each year?

8. (a) Write the dual of the following LPP: (5)

Minimize 16 1 9 2 21 3 Z = x + x + x

Subject to the constraints

x1 + x2 + x3 = 16

2x1 + x2 + x3 ≥12

x1

, x2 ≥ 0

3

x -unrestricted.

7. Use dual simplex method to solve the following LPP. (10)

Min 1 2 2 3 3

z = x + x + x

Subject to

x1 − x2 + x3 ≥

x1 + x2 + 2x3 ≤ 8

x1 − x3 ≥ 2

x1

, x2

, x3 ≥ .0

6. (a) A contractor has to supply 10,000 bearings per day to an automobile manufacturer.

He finds that when he starts production run, he can produce 25,000 bearings per day.

The cost of holding a bearing in stock for one year is Rs. 2 and the set up cost of a

production run is Rs. 180. Find the EOQ. How frequently should the production run

he made? (5)

5(b) A department has five employees with five jobs to be performed. The time (in hours)

each men will take to perform each job is given in the table below: (5)

Employees

I II III IV V

A 10 5 13 15 16

B 3 9 18 13 6

C 10 7 2 2 2

D 7 11 9 7 12

E 7 9 10 4 12

How should the jobs be assigned, one job per employee, so as to minimize the total

man-hours?

5. (a) Use the simplex method to solve the following L.P.P. (5)

Max 4 1 3 2

z = x + x

Subject to

2x1 + x2 ≤1000

x1 + x2 ≤ 800

400 x1 ≤

x2 ≤ 700

.0 , x1

x2 ≥

4. (a) A television repairman finds that the time spent on his jobs has an exponential

distribution with a mean of 30 minutes. If he repairs sets in the order in which they

come in, and if arrival of sets follows a Poission distribution approximately with an

average rate of 10 per 8 hours day, what is the repairman’s expected idle time each

day, How many jobs are ahead of the average set just brought in?