$1$:$37$

Question $1$

Question $1$:

XYZ machine production company has three plants serving four distribution centers. Each plants produces $7,10$ and $18$ machines, respectively. The amount of machine demanded by centers is $5,8,7$ and $15$ machines, respectively. The cost of sending a machine from a plant to a distribution centre is given in the table below. Formulate a balanced transportation problem in a transportation table and show the DP model of the problem to meet the demand of each city at the least cost.

Question $2$:

In an enterprise, product types A and B are produced. This production takes place in three different workshops $($I$,$ II$,$ III$).$ The daily utilization times of the workshops are $8,6$ and $4$ hours respectively. For the production of product A$,1,2,2$ hours of labour is required, while for the production of product B$,2,3,1$ hours of labour is required. Costs of product A and $B$ are $3$ and $4TLs,$ respectively. Accordingly, how many product A and $B$ should the enterprise produce per day in order to produce at minimum cost?

a$)$ Model the problem in linear programming format.

b$)$ Solve the problem with graphical method.

c$)$ Solve the problem with primal simplex method.