Optimization Problem 1
Spinney Manufacturing wants to make baseball hats and visors.
They need to use a cutting machine that is available for only 120 minutes per day.
They also need to use a sewing machine that is available for 60 minutes per day.
Each hat needs 4 minutes on the cutting machine and 3 minutes on the sewing machine.
Each visor needs 3 minutes on the cutting machine and 1 minute on the sewing machine.
The profit on one hat is $1.10 and on one visor is $0.60.
We eventually want to figure out how many hats and how many visors should be made to get
maximum profit.
1. Declare your variables
2. Fill in the following chart.
# of hats ( )
# of visors ( )
Restrictions
Cutting machine
Sewing machine
3. Write the inequations
4. Graph the feasible region
Let the scale be 1 : 10
5. Write an equation to calculate the profit.
Profit =
6. Calculate the profit at each vertex
point in the feasible region
Point ( X , Y )
Profit
(
,
)
(
,
)
(
,
)
7. Answer the question in a full sentence.
1
Optimization Problem 2
The Precision tool company wants to make hammers and chisels.
Each hammer needs 1 hour on machine A and 2 hours on machine B.
Each chisel needs 2 hours on machine A and 1 hour on machine B.
Neither machine can work more than 30 hours per week.
The profit is $3 on each hammer and $2 on each chisel.
We eventually want to find how many of hammers and chisels should be made to get maximum
profit.
1. Declare your variables
2. Fill in the following chart.
# of hammers_____
# of chisels_______
Restrictions
time on machine A
time on machine B
3. Write the inequations
4. Graph the feasible region
5. Write the equation for the profit.
Profit =
6. Calculate the profit at each
vertex
point in the feasible region
Point ( x , y )
Profit
(
,
)
(
,
)
(
,
)
7. Answer the question in a full sentence.
2
Optimization Problem 3
The Ace Manufacturing Company wants to make plates and cups.
Each cup needs 3 hours on machine A and 1 hour on machine B.
Each plate needs 1 hour on machine A and 2 hours on machine B.
Neither machine can work more than 15 hours per day.
The profit is $0.40 on each cup and $0.25 on each plate.
We eventually want to find how many of cups and plates should be made to get maximum profit.
1. Declare your variables
2. Fill in the following chart.
3. Inequation (1) :
Inequation (2) :
4. Graph the feasible region.
5. Profit Equation is
6. Calculate profit
Point ( X , Y )
(
,
)
(
,
)
(
,
)
Profit
7.
Note: In the following questions you could skip step one, if you feel you are ready.
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Optimization Problem 4
A clothing manufacturer makes dresses and suits.
Each suit needs 2 m of silk and 3 m of wool.
Each dress needs 1 m of silk and 2 m of wool.
There are only 100 m of silk and 180 m of wool available.
The profit is $90 on each suit and $50 on each dress.
We eventually want to find how many of suits and dresses should be made to get maximum
profit.
1. Declare your variables
2.
3. Inequations:
Amount of silk used:
Amount of wool used:
4. Graph the inequalities.
5. Equation:
Profit =
6.
Point ( X , Y
(
,
)
(
,
)
(
,
)
)
Profit
7. The clothing manufacturer should
4
Optimization Problem 5
Mrs. Jones wants to bake sponge cakes and angel cakes for a bake sale.
A sponge cake needs 6 eggs and 2 cups of sugar.
An angel cake needs 12 eggs and 1 cup of sugar.
She has only 72 eggs and 9 cups of sugar.
The profit on a sponge cake is $1 and on an angel cake is $2.
How many of each should be made to get maximum profit?
1.
2.
3. Inequations:
4. Graph.
5. Profit =
Point (
,
)
(
,
)
(
,
)
(
,
)
Profit
Mrs. Jones should
5
Optimization Problem 6
The A-1 Clothing Company wants to make shirts and jackets.
Each shirt needs 1 hour on the cutting machine and 2 hours on sewing machine.
Each jacket needs 2 hours on the cutting machine and 1 hour on the sewing machine.
Neither machine can work more than 60 hours per week.
The profit is $10 on each shirt and $15 on each jacket.
How many shirts and how many jackets should be made to get maximum profit?
(x,y)
Profit
6
Optimization Problem 7
The Ace Clothing Company wants to make gloves and mittens.
Each pair of gloves needs 1 hour on the cutting machine and 5 hours on the sewing machine.
Each pair of mittens needs 1 hour on the cutting machine and 1 hour on the sewing machine.
The cutting machine is available for only 60 hours per week.
The sewing machine is available for only 100 hours per week.
The profit is $5 on each pair of mittens and $8 on each on each pair of gloves.
How many pairs of mittens and how many pairs of gloves should be made to get maximum
profit?
Optimization Problem 8
A book case manufacturer wants to make two types of book cases.
Each Model A needs 1 hour in the wood working room and 4 hours in the painting room.
Each Model B needs 2 hours in the wood working room and 1 hour in the painting room
The wood working room is available for only 100 hours per week.
The painting room is available for only 120 hours per week.
The profit is $50 on each Model A and $60 on each Model B.
How many pairs of Model A and how many of Model B should be made to get maximum profit?
Optimization Problem 9
A stereo manufacturer wants to make two types of stereos.
Each Model X needs 2 hours on machine I and 2 hours on machine II.
Each Model Y needs 3 hours on machine I and 1 hour on machine II
Machine I is available for only 120 hours per week.
Machine II is available for only 80 hours per week.
The profit is $100 on each Model X and $120 on each Model Y.
How many pairs of Model X and how many of Model Y should be made to get maximum profit?
Optimization Problem 10
A sports firm makes basketballs and soccer balls. Two machines are used to make the balls and
the time required on each machine is shown
Each day Machine A is available for only 110 min manufacture them while Machine B is available
for 140 min. If the profit on a basketball is $0.90 and on a soccer ball it is $1.30, calculate how
many of each ball should be made each day to get a maximum profit.
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