There are two factories located one at P and the other at Q. From these locations, a certain commodity is to be delivered to each of the three depots…

There are two factories located one at P and the other at Q. From these locations, a certain commodity is to be delivered to each of the three depots situated at A, B and C. The weekly requirements of the depots are respectively $\displaystyle 4$, $\displaystyle 4$ and $\displaystyle 6$ units of the commodity while the production capacity of the factories at P and Q are $\displaystyle 9$ and $\displaystyle 5$ units respectively. The cost of transportation per unit is given as :

Based on the above information, answer the following questions :

Let $\displaystyle x$ units and $\displaystyle \mathrm{y}$ units of the commodity be transported from factory P to the depots at A and B respectively, then

Find (in terms of $\displaystyle x$ and $\displaystyle \mathrm{y}$) how many units of commodity be transported from factory P to depot C.

Find how many units of commodity be transported from factory Q to A, B and C respectively.

Using (i) and (ii), find the total transportation cost $\displaystyle \mathrm{z}$.

Using (i) and (ii), find the constraint inequalities for minimum cost $\displaystyle \mathrm{z}$.