QUESTION ONE $(20$ MARKS$)$

a$.$ Give a detailed description on how to solve a transportation problem using the North$-$

West Corner Method.

b$.$ Define the term balanced transportation problem as used in transportation problem

models.

c$.$ Draw a diagram showing the relationship between the order size, the ordering cost, the

carrying cost and the total associated cost in an inventory management. $[3$ Marks$]$

d$.$ Define operations research and give a brief historical development of operations research.

$[4$ Marks$]$

e$.$ An industry is manufacturing two types of products; product $1$ and product $2.$ The profits

per $Kg$ of the two products are Ksh$.300$ and Ksh$\mathrm{.}400$ respectively. These two products

require processing in three types of machines. The following table shows the available

machine hours per day and the time required on each machine to produce one $Kg$ of Product

$1$ and Product $2.$ Formulate the problem in the form of linear programming problem.