First, in all texts substitute numbers a and b with numbers corresponding to your student code (xxxxxxTVTB). Find the last but one number of the code and add 1, that is  a . Find the last number and add 1 again, that is  b .

For example, let the code be  108671TVTB. The last but one number is  7

The last number is  1

Then the  problem no 1 , for instance, will be

1.      ... then company A will increase its share of the market, at the expanse of B, by 3.2 percent. ...

When wrong parameter values are used the paper will not graded

Home assignment 2

TEM2565

1.      Two competing companies are about to make a decision regarding an investment in a new promotional campaign. Company A considers two alternative courses of action: advertise in all media or in newspapers only. Company B considers also two alternatives: run a sweepstakes or a big sale. If company A advertises in all media and company B runs a sweepstakes, then company A will increase its share of the market, at the expanse of B, by ( ) percent. If company A advertises in all media and company B runs a big sales, then company A will loose ( ) percent of the market. If company A advertises in newspapers only and company B runs a sweepstakes, then company A will loose ( ) percent; and if A advertises in newspapers only and runs a big sale, then A will gain ( ) percent. What fraction of time each alternative should be used by both companies and what is the average gain for company A (or average loss for company B)?

2.      Minimize total inventory costs  when unit holding costs are , unit penalty costs are , and random demand for the product is distributed according to the probability density function

       Obtaining costs are not included.

3.      A refinery has one unloading facility. Ships arriving at the refinery to unload crude oil arrive according to the Poisson distribution with average rate ships per week. Service time is exponential,  days being the average unloading time per ship.

a)      what is the probability for the facility to be idle?

b)      calculate the probability that one ship is serviced and two ships are waiting

c)      what is the average number of ships in the system?

d)     what is the average number of ships waiting to deliver crude oli?

e)      what is the expected time a ship must wait before beginning to deliver its cargo?