In this paper, we have consider the cost of transportation not as of one variable but as multi-variable which includes goods loading charges, vehicle operator charges, on road transportation cost including toll and taxes, maintenance cost of vehicle and goods unloading charges. Then we have solved this multi-variable transportation problem using algebraic approach and compare the result with North – West Corner method

The objective of this paper to combine two Picture Fuzzy Graphs using products namely External direct product and Internal direct product. Also investigate the regularity of these products. Moreover, we discuss some properties such as strongness, connectedness, completeness and complement of Picture Fuzzy Graphs. In this connection the equivalence relation of picture Fuzzy graph is proved.

In this concept, the accurate act of the Dufour and Hall Effect is combined to examine the Magnetohydrodynamic flow past a vertical plate which is exponentially accelerated isothermally with variable mass diffusion is executed. An electrically conducting viscous fluid which is incompressible that doesn’t scatter in any medium is used. To work out the Concentration, Temperature and Velocity factors of the fluid flow, the basic fundamental flow equations are answered using the technique of Laplace Transforms. The Temperature, Concentration and Velocity Profiles explained in the graph are decoded efficiently by applying it in MATLAB. Graph comes out with a rise in wall thickness when there is an increase in time and vice versa for Schmidt number. We can see the same trend in temperature for Df, Sc and t whereas for Prandtl number the temperature is fluctuated. Graph comes out with a decent increase in velocity for the parameters Hall Parameter (m), Mass Grashof Number (Gm), Thermal Grashof number (Gr) and time(t) while on the contrary for Dufour number (Df), Thermal Grashof number (Gr) velocity tends to decrease in a decent way but for Prandtl number (Pr) a fluctuation in velocity can be seen and also when the magnetic field is induced there is an uncertainty in the velocity trend.