Linear Programming Practice Problems
1.
Name: _________________
A small company that makes animals for toy stores uses 1.5 m2 of yellow cloth to
make a lion and 3 m2 to make a giraffe. The lion’s legs require 2.5 m of special plastic
tubing, while the giraffe’s legs require 6 m. The company has in stock 258 m2 of
yellow cloth and 480 m of the plastic tubing. The company makes a profit of $3 for a
lion and $5.50 for a giraffe. How many of each should the company make to maximize
their profit?
y
x
2.
A recipe for bouillabaisse requires 2 qt. stock for 8 servings. A recipe for gumbo calls
for 3 qt. stock for 8 servings. The chef cannot make more than 160 servings a day and
has 54 qt. stock available. If the profit per batch of bouillabaisse is $20 and the profit
per batch of gumbo is $30, find number of batches of each that the chef should make in
order to maximize profit.
y
x
3.
A baker makes bran muffins and corn muffins, which are sold by the box. The baker
can sell at most 20 boxes of bran muffins and 15 boxes of corn muffins per day. It
takes 1 hour to make a box of bran muffins and 1 hour to make a box of corn muffins.
The baker’s team has 30 hours a day to bake muffins. The profit on a box of bran
muffins is $1.25. The profit on a box of corn muffins is $1.35 per box. Determine how
many boxes of each he should bake to maximize his profit.
y
x
CHALLENGE PROBLEM:
Rosa Martinez, who does research for a breakfast food company, wants to blend two grain
mixes to produce a breakfast cereal. Let x be the # of grams of Mix A in a serving and let y
be the # of grams of Mix B. A serving is at most 55g and at least 40g. Mix A is 16% fat and
Mix B is 8% fat. Rosa wants the fat content for a serving to be no more than 6g. Suppose
Mix A costs $.003 per gram and Mix B costs $0.002 per gram to produce. Find the values of
x and y that minimize the cost of one serving.
y
x