How many decision variables are there in a transportation problem which has 5 supply points and 4 demand points Ignore the non-negativity constraints?

Decision Variables

There are 20. When formulating a linear programming problem, it is best have a separate decision variable for each possible decision. Here, we must decide how much to ship from each supply point (5) to each demand point (4), hence we must make 5*4 or 20 decisions.

Constraints

Then, we must come up with the constraint equations bearing on the problem.

Non-negativity

There are real world limitations on the values we may assign to the decision variables. There should almost always be a non-negativity constraint, meaning that no variable can be negative.

Amount available to be shipped from each shipping point

Then the sum of the amount shipped from each shipping point to each demand point must be tallied and set to be greater than or equal to the amount demanded at each demand point.

Amount demanded by each demand point

A similiar set of constraints must be done for each supply point: the sum of the amount shipped from a particular shipping point to each of the four demand points cannot exceed the amount available to be shipped from each shipping point.

Objective function

Finally, a linear programming problem needs an objective function, which will be minimized or maximized. From this formulation, a solution may be possible, depending the the amount demand ed and the amount available to meet the demand.

Tweaks

Shipping costs will vary from each shipping point to each demand point. However, it is also possible, particularly in the real Word, where tariffs, competition, and other market arbitrage opportunities exist, to have not only different costs but also different prices from each shipping point to each demand point. This will lead to a non-linear programming problem, but happily, these are easy to solve as well.

But I digress . . .. You answer is 20.