PROBLEMS
5-1. Q: You operate a small wooden toy company making two products: alphabet blocks and wooden
trucks. Your profit is $30 per box of blocks and $40 per box of trucks. Producing a box of blocks
requires one hour of woodworking and two hours of painting; producing a box of trucks takes
three hours of woodworking but only one hour of painting. You employ three wood workers and
two painters, each working 40 hours per week. How many boxes of blocks (B) and trucks (T)
should you make each week to maximize profit? Solve graphically as a linear program and
confirm analytically.
A: The problem is to choose the number of boxes of blocks B and trucks T to maximize weekly
5-2. Q. A commercial orchard grows, picks, and packs apples and pears. A peck (quarter bushel) of
apples takes four minutes to pick and five minutes to pack; a peck of pears takes five minutes to
pick and four minutes to pack. Only one picker and one packer are available. How many pecks
each of apples and pears should be picked and packed every hour (60 minutes) if the profit is
$3/peck for apples and $2/peck for pears? Solve graphically as a linear program and confirm
analytically.
A: As the graph below show, the solution for pecks of (apples a, pears p) must be: (12,0), for a profit P =