Math 141 WIR, Spring 2007,cBenjamin AurispaMath 141 Exam 1 Review Problem SetNote: Not every topic is covered in this review. Please also take a look at the previousWeek in Reviews for more practice problems.1. Find the equation of the line that is parallel to the line 2x − 3y = 12 and passes through thex-intercept of the line y = −7x + 6.2. Find the value of n that makes the following lines perpendicular.4x − 9y = −76x + ny = 103. A keychain company incurs fixed costs of $1500 every month and it costs them $2 to make eachkeychain. When 300 keychains are sold, the company earns revenue of $1800.(a) What is the selling price of a keychain?(b) What is the profit function for this company?1Math 141 WIR, Spring 2007,cBenjamin Aurispa(c) What is the break-even point?4. A wilderness store finds that when the price of a tent is $53, 176 people are willing to buy it,but the supplier is only willing to supply 152 tents. When the price increases by $8, only 112people are willing to buy the tent, but the supplier is willing to supply 32 more tents than atthe $53 price.(a) Find the supply and demand equations.(b) What is the market equilibrium (equilibrium point)?2Math 141 WIR, Spring 2007,cBenjamin Aurispa5. Suppose data was gathered of how many McDonald’s (in thousands) there were in Texas from2002-2006. The results are given in the table below.Year 2002 2003 2004 2005 2006McDonald’s 9 11 13 10 11(a) Find the least-squares line for this data where x is the number of years since 2002 and yis the number of McDonald’s in thousands.(b) Predict how many McDonald’s there will be in Texas in 2009.(c) In what year would you expect there to be 15000 McDonald’s in Texas?(d) How well does the line fit the data?6. For the following augmented matrices, state whether the matrix is in row-reduced form or not.If the matrix IS in row-reduced form, tell how many solutions to the system there are. Ifit is NOT in row-reduced form, state the NEXT row operation needed to get the matrix inrow-reduced form.(a)1 0 4 50 1 −3 60 0 0 1(b)1 9 0 60 1 0 70 0 0 0(c)1 0 −70 1 80 0 03Math 141 WIR, Spring 2007,cBenjamin Aurispa(d)1 0 60 1 20 1 5(e)"1 0 40 3 9#(f)"1 0 1 10 1 3 2#7. Use the Guass-Jordan method to get the following matrix in row-reduced form."4 8 32−3 −5 −18#8. Kristina drinks both Coke and Pepsi. A 20 oz bottle of Coke contains 58 mg of Caffeine and243 calories. A 20 oz bottle of Pepsi contains 63 mg of Caffeine and 250 calories. In a givenweek, Kristina drinks enough Cokes and Pepsis to take in 1326 mg of Caffeine and 5416 calories.How many Cokes and Pepsis did Kristina drink that week?4Math 141 WIR, Spring 2007,cBenjamin Aurispa9. Solve the following systems of equations. If there are infinitely many solutions, make sure toparameterize the solution.(a) 10x − 8y = 6−15x + 12y = 20(b) 2x + y + z = 54x + 6z = 14 + 2y−6x + 3y − 9z = −2110. Solve for the variables in the following equation.3"1 −2−4 9#−1+"−5 a2b 6#T="−1 c + 19d 20#"0 21 0#5Math 141 WIR, Spring 2007,cBenjamin Aurispa11. John is throwing a Super Bowl party and wants to oder pizzas. He finds that Papa John’scharges $6 for a small pizza, $9 for a medium pizza, and $12 for a large pizza. Pizza Hut charges$5 for a small pizza, $10 for a medium pizza, and $13 for a large pizza. This information issummarized in the following matrix.A=PJ PHSML6 59 1012 13If John wants to order 5 small, 3 medium, and 6 large pizzas, find a matrix B so that whenmultiplied with A will give the total cost of his order if he orders from Papa John’s or if heorders from Pizza Hut. Then do the matrix multiplication.12. Given the following matrices and their sizes, determine whether the matrix operations arepossible or not possible.A2×4B3×2C4×3D3×3E2×3(a) 4AC + E(b) BA + C(c) ATE − 7C(d) BED(e) DBT6Math 141 WIR, Spring 2007,cBenjamin Aurispa13. Suppose there are 3 major airlines that fly out of Houston: Southwest, Delta, and American.A Southwest flight holds 135 people, a Delta flight holds 160 people, and an American flightholds 148 people. On a given day, a total of 88,683 people flew out of Houston. There were 3times as many Southwest flights as Delta flights, and the number of American flights was halfthe number of Southwest and Delta flights combined. How many flights out of Houston werethere for each airline?(a) Set up this problem.(b) Write the system of equations as a matrix equation AX = B.(c) Solve the matrix equation using matrix inverses.7Math 141 WIR, Spring 2007,cBenjamin Aurispa14. (Note: This problem is from 2.7 which all instructors may not cover.) A simple economy consists of3 industries: Agriculture, Transportation, and Service. The production of 1 unit of agriculturalproducts requires the consumption of 0.2 units of agricultural products, 0.1 units of transporta-tion, and 0.1 units of service goods. The production of 1 unit of transportation requires theconsumption of 0.3 units of agricultural products, 0.4 units of transportation, and 0.3 units ofservice. Finally, the production of 1 unit of service goods requires the consumption of 0.2 unitsof agricultural products, 0.1 units of transportation, and 0.3 units of service.(a) Find the Input-Output matrix A.(b) Find the gross output of goods needed to satisfy consumer demand for 790 units of agri-cultural products, 445 units of transportation, and 205 units of service goods.(c) Find the value of goods consumed in the internal process of production in order to meetthe above gross
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