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**Unformatted text preview: **MAC1105 Lectui‘e Worksheet 6 F all, 2011
Solving Systems of Linear Equations and Inequalities, Business Applications 1. Solve each system, Showing all algebraic details. Check solution points. x~y=—4r ' 4x—8y=16 a) x y b) 1
—+.—.:3 =H.—2
2 3 y 216 2. If a system of two linear equations in variables X and y has no solutions, the lines must be (parallel I perpendicular / coinciding) 3. Part of a $3000 investment is placed in stocks, and the rest in bonds. The stocks earn 4.5%
annual interest while the bonds 8% annual interest. If the total interest earned is $177, how much
was invested in stocks? $ In bonds? $ 4. The total cost to heat a large building over a period of time is the initial (one—time, at the beginning)
cost to purchase and install the heating system (called the ﬁxed cost), plus the monthly cost for energy.
The table below shows these costs for a gas heating system and a solar heating system. Fixed Cost Monthly Energy Cost
Gas: $12,000 Gas: $700 per month
Solar: $30,000 Solar: $150 per month How many months (rounded to the nearest tenth of a month) will it take for the two systems to be equal in
cost? Answer: Approximately months. 5. A large wholesale nursery grows shrubs and sells them to retail stores. The nursery’s ﬁxed costs toal
$12,000, and it costs the nursery about $15 to plant, cultivate, and harvest each shrub. The nursery charges the retail stores about $19 per shrub. a) Write formulas for the cost function, C(x), and the revenue function, R(x), for x shrubs. Answers: C(X) = R00 : b) Find both coordinates of the break—even point algebraically, and write a sentence that intetprets
this point. 6) Sketch the revenue and cost functions for x 2 0 , labeling the break—even point with both
coordinates. 6. Sketch and shade the solution set for each system of inequalities: <5mx~3 2xey>3 y j a) b) x50
y22 y>0 7. Write the system of inequalities that is represented by the graph below. 8. Let C(x) and R(X) represent the 'cost and revenue functions for x units of some product. The region
where revenue is greater than or equal to cost is called the proﬁt region. Go back to your graph for #5 and shade the proﬁt region. ...

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