Our manufacturing plant produces bookshelves, couches, and workta-
bles. we have 400 hours of labor that are available to us each week, and 1000
units of lumber as raw materials. each bookshelf produced yields a prot of $6,
consumes 12 hours of labor, and 40 units of lumber. each couch yields a prot of
$5, consumes 14 hours of labor, and 22 units of lumber. each worktables yields a
prot of $8, consumes 16 hours of labor, and 60 units of lumber. write a linear
program to determine how many bookshelves, couches, and worktables should be
produced to maximize prots, subject to labor and lumber restrictions. (you may
allow fractional production; do not compute the optimal solution.)