Reference no: EM131290323

Question one

A manufacturer is to market a new fertilizer which to be a mixture of two ingredients A and B. the properties of the two ingredients are given in the table:

	Bone meal	Nitrogen	Lime	Phosphates	Cost(Shs)/kg
Ingredient A	20%	30%	40%	10%	12
Ingredient B	40%	10%	45%	5%	8

It has been decided that:

• the fertilizer will be sold in bags containing 100kgs
• it must contain at least 15% nitrogen
• it must contain at least 8% phosphates
• it must contain at least 25% bone meal

The manufacturer wishes to meet the above requirements at the minimum cost possible. Formulate a linear programming model for the problem and apply graphical method to solve it (6 marks)

Question two

Solve the following linear program by simplex method

Minimize 

Subject to    (6 marks)

Question three

A marketing manager has five salesmen all of different  capabilities, The salesmen are to be deployed to five districts, the estimates made by the marketing manager for the sales per month (10,000 shillings) for each salesman in each district would be as follows.

		District
Salesman	A	B         C	D	E
1	32	38        40	28	40
2	40	24        28	21	36
3	41	27        33	30	37
4	22	38        41	36	36
5	29	33        40	35	39

Find the assignment of salesmen to the districts that will result in maximum sales.(5marks) 

Question four

A self-service store employs one cashier at its counter. 9 customers arrive on an average every FIVE minutes while the cashiers can serve 10 customers in FIVE minutes. Assuming Poisson distribution for arrival rate and exponential distribution for service times, find;

(i)Average number of customers in the system.

(ii)Average number of customers in the queue.                                           

(iii)Average time a customer spends in the system.

Question five

A Company ltd is planning to open a new branch to grow its business. The administration is treating the move as a project to be undertaken. The following activities together with their related data have been identified.

Activity	Preceding Activity	Time in Days Optimistic                    Most likely            Pessimistic Time                                   Time                      Time
A B C D E F G H I J K	- A A B C D C F,E G H,I J	6                                             9                      12 6                                             8                       10 3                                             7                       11 12                                           16                      20 6                                             11                      22 12                                           15                      24 5                                              7                       15 4                                             8                        12 6                                             8                        10 14                                          28                       48 6                                              6                       24

 

Required:-

 

a)      Draw a network to represent the above data

b)      Determine the critical path of the project and the expected project length

c)      Calculate the  floats for each activity if any