Question 536571
The time required for assembling x bikes and y wagons is {{{3x+4y}}}
The time required for painting x bikes and y wagons is {{{5x+7y}}}
The profit from x bikes and y wagons is {{{P=20x+34y}}}
The constrains are {{{x>=0}}} {{{y>=0}}} {{{3x+4y<=400}}} {{{5x+7y<=300}}}
The first two tell you that you will not produce a negative number of bikes or a negative number of wagons, so your feasibility region excludes anything to the left of the y-axis and/or below the x-axis. The other two boundaries are lines that cross the positive x- and y-axis. If those two lines may intersect at a point  with positive x and y, that point will be a corner of the feasibility region.
{{{graph( 400, 400, -50, 150, -50, 150, 100-3x/4, 300/7-5x/7 )}}} The green line represents {{{5x+7y=300}}} (painting time constraint), the blue one {{{3x+4y=400}}} (assembling constraint)
Unfortunately, your feasibility region is the triangle between the green line and the axes. It seems to be that no matter how many items you can assemble, the painting is your bottleneck. If possible, expand the painting section of the shop and hire more painters.