Math 141 WIR, Spring 2007,cBenjamin AurispaMath 141 Week-in-Review 2 Problem Set1. A DVD company incurs $3,000 in fixed costs each month and production costs of $8 per DVD.The company earns a profit of $4,200 when they sell 600 DVDs in a month.(a) What is the selling price of a DVD?(b) What is the profit function for this company?(c) What is the break-even point?2. An office goods store found that they can sell 90 pens per week if they cost $1, but if theyincrease the price by $1, then only 30 pens are sold. However the suppliers are only willing tosupply 60 pens when the unit price is $2, and will not supply any pens if the unit price is $1or below.(a) Find the supply and demand equations (assuming they are linear).1Math 141 WIR, Spring 2007,cBenjamin Aurispa(b) Find the market equilibrium.3. A study was done concerning the relationship between the average number of hours a studentspends on MySpace in a day and their GPA at the end of the semester. The results are givenin the following table. (Note: I made this up. It is not a real study.)Hours, x 0 1 2 3 4 5GPA, y 3.5 3.2 3.0 2.6 2.5 2.1(a) Find the least-squares line that models this data. (Round to 4 decimal places.)(b) How well does the line fit the data?(c) Predict the GPA of a student who spends on average 6.5 hours a day on MySpace.(d) How many hours a day would you expect a student with a GPA of 3.1 to have spent onMySpace?4. Solve the following systems of equations.(a) 3x − y = 76x + 2y = 102Math 141 WIR, Spring 2007,cBenjamin Aurispa(b) 4x − 2y = 68x − 4y = 165. Find the value of k which makes the following system of equations have infinitely many solu-tions.2x + 8y = −83x + ky = −126. Suppose I had a drink stand where I sold bottles of lemonade, Koolaid, and Gatorade. I soldeach bottle of lemonade for $1.25, each bottle of Koolaid for $1.75, and each bottle of Gatoradefor $2.50. At the end of a certain day, I had sales of $254. In all I had sold 158 bottles, and Iknew that I sold three times as many lemonade bottles as Gatorade bottles. How many bottlesof each drink did I sell? Set up and solve this problem.3Math 141 WIR, Spring 2007,cBenjamin Aurispa7. Freebirds offers regular, monster, and super monster burritos. A regular burrito gets 1 servingof rice, 2 servings of beans, and 1 serving of meat. A monster burrito gets 2 servings of rice, 2servings of beans, and 2 servings of meat. A super monster gets 3 servings of rice, 3 servings ofbeans, and 4 servings of meat. Suppose that Freebirds has 1085 servings of rice, 1410 servingsof beans, and 1195 servings of meat availabe. If all of the available servings are used on a givenday, how many of each size of burrito were made? Set up and solve this problem.8. State whether the following matrices are in row-reduced form. If the matrix is NOT in row-reduced form, what would be the next row operation needed in the Gauss-Jordan EliminationMethod?(a)1 0 0 20 1 0 30 1 2 4(b)"1 2 0 30 0 1 4#(c)"1 2 30 1 −2#(d)1 0 0 20 −1 3 −40 0 0 04Math 141 WIR, Spring 2007,cBenjamin Aurispa9. Pivot the following matrix about the boxed element. Indicate the row operations used.1 2 4 −30 3 −9 120 −5 2 110. Solve the following systems of equations. If there are infinitely many solutions, make sure youparameterize the solution.(a) x = −z − 2x + y + z = −23x + 2y + 2z = −3y = 2 − 2x5Math 141 WIR, Spring 2007,cBenjamin Aurispa(b) x + 2y + z = 33x + 3y + 3z = 72x + y + 2z = 1(c) 2x + y − z = 0x − 3y + z = 1x + 4y − 2z = −1(d) x + 2y + z − 3w = 4−2x + y + z + w = 2−x + 3y + 2z − 2w =
View Full Document
Unlocking...