(Use the graphical method for the following problem): A
furniture manufacturer makes couches and recliners. The following
table gives the labor requirements and profits per piece of
furniture:
couches
recliners
design assembly
6 labor hours
3 labor hours
12 labor hours
1 labor hour
profit
$150
$120
Each day, a total of 480 labor hours are available to design and
60 labor hours are available to assemble. The manufacturer wants to
determine how many pieces of furniture to produce of each type in
order to maximize profit.
(a) Define variables for modeling this scenario and write down
the objective function.
(b) Identify the constraint inequalities for this problem.
(c) List the corner points for the feasible region (you do not
need to include a picture of your graph in your work).
(d) How many couches and recliners should be produced each day
to maximize profit? And, what is the maximum profit?