# Purchase And Sell Problem In Linear Programming

**Introduction:**

It is well known fact that the transportation problem is cost minimization model, i.e. we have to find the least cost transportation schedule for the given problem. Sometimes the cost will become secondary factor when the time required for transportation is considered.

**Purchase and sell problem:**

**Example: ****M/S Epsilon traders purchase a certain type of product from three manufacturing units in different places and sell the same to five market segments. The cost of purchasing and the cost of transport from the traders place to market centers in Rs. per 100 units are given below:**

**The trader wants to decide which manufacturer should be asked to supply how many to which market segment so that the total cost of transportation and purchase is minimized.**

**Solution:**

Here availability is 300000 units and the total requirement is 320000 units. Hence a dummy row (*D*) is to be opened. The following matrix shows the cost of transportation and purchase per unit in Rs. from manufacturer to the market centers directly.

Let us multiply the matrix by 100 to avoid decimal numbers and get the basic feasible solution by VAM.

**Table. Avail: Availability. Req: Requirement, Roc: Row opportunity cost, Coc: Column opportunity cost.**