Your second solution hits the correct answers. Having a fixed mix of 1:4 lets you think of this one in terms of 'packages', with each package consisting of 1 chair and 4 stools. Each package has a unit sales price of 250, and a unit variable cost of 105.
I haven't vetted your first solution in detail, but at a glance it looks like you're trying to weight the chairs:stools at 25:75 instead of 20:80. Fix your weights accordingly and both of your approaches will probably agree.