1.A cement company has three factories
which manufacture cement at which is the transported to four distribution
centres. The quantity of monthly production of each factory, the demand of each
distribution centre and the associated transportation cost per unit are given
as follows:

i.Suggest the optimal transportation schedule
ii.Is there any other transportation schedule which is equally
attractive? If so, write that.
iii. If the company wants at least 5000 units 5000 units of cement are
transported from factory C to distribution centre Y, will the transportation
schedule be any different? If so, what will be the new optimal schedule and the
new optimal schedule and the effect on cost?
iv.Suppose the company desires to send at most 500 units of cement from
factory C to distribution centre Y, what will the optimal schedule be? Also,
obtain the total transportation cost in such a case.

2. Smith Corporation has four salesmen each of them can be assigned any of
the four sales territories. Estimates of the sales revenues in hundreds of
shillings for each salesman are as given below:

Required
i). Obtain the optimal assignments that maximizes the sales revenue
ii).Build a linear programming problem
3. An Indian oil company is considering whether to go for an off shore
drilling contract to be awarded in Bombay. If they bid, value would be sh. 600
million with 65% chance of gaining the contract. The company may set up a new
drilling operation or move already existing operation, which has proved
successful, to new site. The probability of success and expected returns are as
follows:

If the company does not bid or lose the contract, they can use sh. 600 million
to modernize their operations. This would result in a return of either 5% or 8%
on the sum invested with probabilities 0.45 and 0.55 respectively.
a.Construct a decision tree for the problem showing clearly the course
of action.
b.By applying an appropriate decision criteria recommend whether or not
the company should bid the contract.

4.In a small town there are only two stores that handle sundry goods-
Patel ltd and Smith ltd. The total number of customers is equally divided
between the two, because price and quality of goods sold are equal. Both stores
have a good reputation in the community and they render equally good customer
service. Assume that a gain of a customer by Patel ltd is a loss to Smith ltd
and vice versa. Both stores plan to run annual Christmas sales during the
second week of December. Sales are advertised through a local newspaper, radio
and television media. With the aid of an advertising firm, the store, Patel ltd
constructed the following game matrix.

Determine the optimal strategies and the worth of such strategies for both
Patel ltd and Smith ltd.
5.The following list of activities must be accomplished in order to
complete a construction project:

i).Construct a network and find the critical path and duration for the
project
ii).At the end of 10 weeks, the progress is:
• Activities completed: A, B and E.
• Activities not started: C, D, F, G, H, I and J.
If no action is taken at all, when will the project get completed?
iii).What action will you take so that the project is completed by the
end of week 42?

Attachments:

Operations-Re….docx