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Systems of inequalities Jeopardy PowerPoint Presentation

Systems of inequalities Jeopardy

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### Systems of inequalitiesJeopardy

By Myia, Erin, and Maddy

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Category 3200 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

200 points

x: number of scientific calculators producedy: number of graphing calculators produced

Y=170

X=200

X=100

Y=80

Y=-X+200

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Category 3300 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

300 Points

x: amount (in thousands) invested in bondsy: amount (in thousands) invested in CDs

MaximizeY = 1.44 – 0.05x – 0.04y, subjectto: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 bondsy: 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 givey< ( 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 3400 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

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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