3 4 HW Day 2 - Linear Programing - Word Problems

Algebra II Academic
Name: _____________________________
3.4 HW - Linear Programming Day 2 October 17, 2013 Period: ______
Define variables, write the system of constraints & objective function, then graph and solve.
1. Air Quality Trees in urban areas help keep air fresh by
absorbing carbon dioxide. A city has $2100 to spend on
planting maple and spruce trees. The land available for
planting is 45, 000 ft 2 . How many of each tree should the
city plant to maximize carbon dioxide absorption?
Define the variables. ____________ _____________
y
Constraints:
Objective Function: ______________
Vertices: ___________________
# of Maple trees: _______ # of Spruce trees: _______
(0,0)
*Count by 5’s
x
2. Baking a tray of corn muffins takes 4 c. milk and 3 c. wheat flour. A tray of bran muffins takes 2 c. milk and
3 c. wheat flour. The baker makes $3 profit per tray of corn muffins and $2 profit per tray of bran muffins. He
only has 16 cups of milk and 15 cups of wheat flour. How many trays of each type of muffin should the baker
make to maximize his profit?
Define the variables. ____________ _____________
Constraints:
Objective Function: ______________
Vertices: ___________________
# of tray corn: _______ # of tray bran: _______

3. You are going to make and sell bread. A loaf of Irish soda bread is made with 2 cup flour and ¼ cup sugar.
Kugelhopf cake is made with 4 cup flour and 1 cup sugar. You will make a profit of $1.50 on each loaf of Irish
soda bread and a profit of $4 on each Kugelhopf cake. You have 16 cup flour and 3 cup sugar. How many loafs
of each type of bread should you bake to maximize profits?
Define the variables. ____________ _____________
Constraints:
Objective Function: ______________
Vertices: ___________________
# of loaves Irish Soda: _______ # of loaves Kugelhopf: _______
4. Suppose you make and sell skin lotion. A quart of regular skin lotion contains 2 cup oil and 1 cup cocoa
butter. A quart of extra-rich skin lotion contains 1 cup oil and 2 cup cocoa butter. You will make a profit of
$10/quart on regular lotion and a profit of $8/quart on extra-rich lotion. You have 14 cup oil and 16 cup cocoa
butter. How many types of each lotion should you make to maximize profits?
Define the variables. ____________ _____________
Constraints:
y
Objective Function: ______________
Vertices: ___________________
# of regular: _______ # of extra-rich: _______
(0,0)
x

5. You need to buy filing cabinets. Cabinet X costs $10 per unit, requires six square feet of floor space, and
holds eight cubic feet of files. Cabinet Y costs $20 per unit, requires eight square feet of floor space, and holds
twelve cubic feet of files. You have been given $140 for this purchase. The office only has room for 72 square
feet of floor space available. How many of each should you buy to maximize storage volume?
Define the variables. ____________ _____________
y
Constraints:
Objective Function: ______________
Vertices: ___________________
# of cabinet X: _______ # of cabinet Y: _______
(0,0)
x
6. Suppose Anna is making scarves and hats for a sale. She only has time to make seven items before the sale.
She only has 4 pom-poms so she can only make 4 hats. Scarves sell for $15 and hats sell for $10. What
combination of scarves and hats should she make to maximize profits?
Variables: _________________ & __________________
Constraints:
⎧
⎪
⎨
⎪
⎩
Objective Function: ___________________
---- Circle one: Max or Min
7. Cindy’s making sets of earrings and necklaces to earn money. Each set of earrings uses two jewels and sells
for $1. Each necklace uses one jewel and sells for $2. She only has 300 jewels and she only enough twine to
make 200 items. What combination of earrings and necklaces could she make to maximize profits?
Variables: _________________ & __________________
Constraints:
⎧
⎪ ⎨⎪⎩
Objective Function: ___________________
---- Circle one: Max or Min
8. A wood shop makes $3 on each small trinket and $7 on each large trinket. On a typical week, it sells
between 500 and 750 small trinkets and between 600 to 1250 large trinkets. The shop can make no more
than 1750 trinkets in a day. What combination of trinkets should be made to maximize profits?
Variables: _________________ & __________________
Constraints:
⎧
⎪ ⎨⎪⎩
Objective Function: ___________________
---- Circle one: Max or Min