Linear Programming
Math 156
Names:
A manufacturing firm makes two types of water skis, a trick ski and a slalom ski. Two processes are
involved in making both types of skis. The fabricating department takes 6 hours to make a trick ski and 4
hours to make a slalom ski and has 108 labor-hours available. The Finishing Department spends 1 hour
finishing for either type of ski and has 24 labor-hours available. If the profit on a trick ski is $40 and the
profit on a slalom ski is $30, how many of each type of ski should be manufactured to realize a maximum
profit? What is the maximum profit?
A manufacturing plant makes two types of inflatable boats, a two-person boat and a four-person boat. Each
two-person boat requires 0.9 labor-hours from the cutting department and 0.8 labor-hours from the
assembly department. Each four-person boat requires 1.8 labor-hours from the cutting department and 1.2
labor-hours from the assembly department. The maximum labor-hours available per month in the cutting
department and the assembly department are 864 and 672, respectively. The company makes a profit of
$25 on each two-person boat and $40 on each four-person boat. How many boats of each type should be
made in a month in order to maximize profit? What is the maximum profit?