Transcript Systems of inequalities Jeopardy

SYSTEMS OF INEQUALITIES
JEOPARDY
By Myia, Erin, and Maddy
Category 1
Category 2
Category 3
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CATEGORY 1
200 POINTS
What is the value of Y in the equation
when X =0
Y<X+6
Answer
Y<6
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Category 1
300 Points
What is the Y value of Y>6X-5 when
X=2
Answer
Category 1
300 points
Y>7
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CATEGORY 1
400 POINTS
What is the value of Y in the Equation Y>X15+-5 when
X=10
Answer
Category 1
400 Points
Y>145
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CATEGORY 2
200 POINTS
Solve the system by graphing
it
2x – 3y < 12
x + 5y < 20
x>0
Answer
Category 2
200 Points
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CATEGORY 2
300 POINTS
Solve the system by
graphing it
2x – y > –3
4x + y < 5
Answer
Category 2
300 points
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CATEGORY 2
400 POINTS
Solve the system by graphing it
x – y < –2
x–y>2
Answer
Category 2
400 Points
No Solution
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CATEGORY 3
200 POINTS
A calculator company produces a scientific calculator and a graphing
calculator. Long-term projections indicate an expected demand of at
least 100 scientific and 80 graphing calculators each day. Because of
limitations on production capacity, no more than 200 scientific
and 170 graphing calculators can be made daily. To satisfy a shipping
contract, a total of at least 200 calculators much be shipped each day.
If each scientific calculator sold results in a $2 loss, but each
graphing calculator produces a $5 profit, how many of each type
should be made daily to maximize net profits?
Answer
Category 3
200 points
x: number of scientific
calculators produced
y: number of graphing
calculators produced
Y=170
X=200
X=100
Y=80
Y=-X+200
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CATEGORY 3
300 POINTS
You have $12,000 to invest, and three different funds from which to
choose. The municipal bond fund has a 7% return, the local bank's CDs
have an 8% return, and the high-risk account has an expected (hoped-for)
12% return. To minimize risk, you decide not to invest any more than
$2,000 in the high-risk account. For tax reasons, you need to invest at
least three times as much in the municipal bonds as in the bank CDs.
Assuming the year-end yields are as expected, what are the optimal
investment amounts?
Answer
Category 3
300 Points
x: amount (in thousands)
invested in bonds
y: amount (in thousands)
invested in CDs
Maximize Y =
1.44 – 0.05x –
0.04y, subject to:
x>0
y>0
y > –x + 10
y < –x + 12
y < ( 1/3 )x
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Explanation
Since the question is asking to find the amount of money for each
account, the variables will need to stand for those amounts. Since its
easier to deal with smaller numbers, count by thousands
x: amount (in thousands) invested in bonds
y: amount (in thousands) invested in CDs
only have two variables, but have three accounts. To handle this,
they need the “How much is left" construction:
12 – x – y: amount (in thousands) invested in the high-risk account
can't invest negative amounts of money, so the first two constraints
are the usual ones: x > 0and y > 0. The amount in the high-risk
account can't be negative either, so 12 – x – y > 0, which simplifies as:
y < –x + 12
The upper limit on the high-risk account gives the
inequality
(12 – x – y) < 2. This simplifies as: y > –x + 10
And the tax requirements give y < ( 1/3 )x. The optimization equation
will be the total investment yield, Y = 0.07x + 0.08y + 0.12(12 – x – y)
= 1.44 – 0.05x – 0.04y.
CATEGORY 3
400 POINTS
The "We Sell CDs" website plans to purchase ads in a
local newspaper advertising their site. Their
operating budget will allow them to spend at most
$2200 on this advertising adventure. They plan to run
at most 20 ads. An ad will cost $50 to appear in the
weekday paper and $200 to appear in a weekend
edition. Prepare a graph that will represent all of the
possible combinations of ads under these conditions
Answer
Category 3
400 Points
x + y < 20 (there will be
at most 20 ads)
200x + 50y < 2200 (the
cost of the ads at most
$2200)
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