Linear Programming
February 6, 2012
Notes
1. Snack Bar A college snack bar cooks and sells hamburgers and hotdogs during the lunch
hour. To stay in business it must sell at least 10 hamburgers but cannot cook more than 40.
It must also sell at least 10 hotdogs but cannot cook more than 70. The college snack bar
cannot cook more than 90 snacks all together. Given that the profit on a hamburger is $0.33
and on a hot dog is $0.21, determine the combination of the number of hamburgers and hot
dogs that will maximize their profit.
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Linear Programming
February 6, 2012
2. Golf Clubs A manufacturer of golf clubs produces sets of Deluxe model clubs and Pro
model clubs. The manufacturer makes a profit of $50 per set on a model Deluxe set and
$45 per set on a model Pro set. The daily production of Deluxe model clubs is between 30
and 50 sets, inclusive, and that of the Pro model clubs is between 10 and 20 sets, inclusive.
The total daily production is not to exceed 50 sets. Determine the combination of deluxe
and pro sets that will maximize their profit.
SHOW ALL WORK.
for your use.
Use a separate sheet of paper if necessary. A graph is included
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Linear Programming
February 6, 2012
3. Carmella and Walt produce handmade shawls and afghans. They spin the yarn, dye it, and
then weave it. A shawl requires 1 hour of spinning, 1 hour of dyeing, and 1 hour of weaving.
An afghan needs 2 hours of spinning, 1 hour of dyeing, and 4 hours of weaving. Together,
they spend at most 8 hours spinning, 6 hours dyeing, and 14 hours weaving daily. They
make $10 profit per shawl and $20 profit per afghan. Determine the combination of afghans
and shawls that will maximize their profit. Below is a graph that may be used to answer this
question. Show all work.
a. Define the variables.
b. Write the objective function.
c. Write the inequalities (constraints) to describe the situation. (Hint: There should be 5
inequalities)
d. Graph and shade the solution set (feasible region). Find all corner points and label
the coordinates on the graph. (Hint: Be sure to graph accurately. There should be 5
corner points)
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e. Determine the final answer. Show all mathematical work. Use a complete sentence
to answer this question.
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Linear Programming
February 6, 2012
4. A potter is making cups and plates. It takes her 6 minutes to make a cup and 3 minutes to
make a plate. Each cup uses 3/4 lb. of clay and each plate uses one lb. of clay. She has 20
hours available for making the cups and plates and has 250 lbs. of clay on hand. She makes
a profit of $2 on each cup and $1.50 on each plate. How many cups and how many plates
should she make in order to maximize her profit?
a. Define the variables.
b. Write the objective function.
c. Write the inequalities (constraints) to describe the situation.
d. Graph and shade the solution set (feasible region). Find all corner points and label
the coordinates on the graph.
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e. Determine the final answer. Show all mathematical work. Use a complete sentence
to answer this question.
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