Question

using the graphical method solve the following linear programing problem maxmise objective function p=3x+y.subject to following constrains 6x+4y<48:3x+6y<42 x>0;y>0

Answer 1

Graphaical method, a piece of cake.

Y upward axis, x horizontal.

plot the line 6x+4y=48
y=-3/2 x+12 Your area of interest will be blow this line.
Plot the line 3x+6y<42 or
y=-1/2 x +7
your area of interest will be below this line.
Mark the lines x=0, y=0, that gives you four lines, which encloses an area of possible solution.
Now a neat theorem of linear programming is that your objective function will be optimized at one of the corners. So test each corner for the value of P. Wherever max, that is the solution.
Neat and tidy, like Red Velvet Cake.