Question 984090
{{{x}}}= number of chairs made
{{{y}}}= number of desks made
{{{5x+8y}}}= time (hours) required for a carpenter to make {{{x}}} chairs and {{{y}}} desks.
So, {{{highlight(5x+8y<=400)}}} , because the carpentry department has enough people to work up to 400 hours per week.
{{{2.5x+2y}}}= time (hours) required for a finisher to paint {{{x}}} chairs and {{{y}}} desks.
So, {{{highlight(2.5x+2y<=120)}}} , because the finishing department can put 120 hours per week.
(a.) The system of inequalities to model the situation is
{{{highlight(system(5x+8y<=400,2.5x+2y<=120))}}}
(b.) The graph for the system is shown below.
The solution is the quadrilateral shaded.
{{{drawing(300,300,-10,90,-10,90,
grid(1),
red(line(-16,60,96,-10)),
green(line(-12,75,60,-15)),
blue(line(4,0,4,47.5)),
blue(line(8,0,8,45)),
blue(line(12,0,12,42.5)),
blue(line(16,0,16,40)),
blue(line(20,0,20,35)),
blue(line(24,0,24,30)),
blue(line(28,0,28,25)),
blue(line(32,0,32,20)),
blue(line(36,0,36,15)),
blue(line(40,0,40,10)),
blue(line(44,0,44,5))
)}}}