University of Maryland University MATH 106 4010 Quiz 3 (2015)

Directions:- Read and sign the academic honesty certification statement below, then read the questionscarefully and answer them to the best of your ability. You may write your answers on this sheetor on the sheet you do your work on, but PLEASE show your work! Follow directions asoutlined in Unit Quiz 3 folder under the Assignments link on our LEO classroom NavBar.- Test & work is due as specified in Course Schedule. I cannot accept any late submissions!This is open-book and notes; calculators & graphing aids are authorized for use. Good luck!I certify the work submitted on and with this document represents my own personal work. I havenot collaborated with, or consulted with, anyone else to produce the work I am submitting. Icertify I have not used any instructor solutions manuals, or any online problem solving services.I understand and agree to abide by UMUC Policy on Academic Dishonesty and Plagiarism._______________________________________Student Signature & DateShow your work!Evaluate manually and write/type it on the quiz document, orProvide scan/image of work done on calculator, orInsert chart/graphic if using softwareIf using augmented matrix methods, be sure to indicate the exact row operations used totransform matrix into row-equivalent matrix (e.g., 31 1 )******************************************************************************1. Multiple Choice: When solving a system of linear equations with the unknowns 1 and 2the following reduced augmented matrix resulted:[106 2|]0 0What can be concluded about the solution of the system?a.b.c.d.Only one solution to the system: 1 = 2 and 2 = 0.No solutions to the system.Infinite solutions; the solution is 1 = 6t + 2 and 2 = t, for any real number t.Infinite solutions; the solution is 1 = 6t + 2 and 2 = t, for any real number t.Answer: _____________________12. Solve following system of linear equations with augmented matrix methods. Show all work!3 2 = 72 + 3 = 3Answer: _________________________________*************3. You are the chief financial officer for Freestate Power & Light, an energy company producingelectricity for greater Megalopolis. Your electric plant runs on natural gas provided by GalacticGas, an energy company supplying greater Megalopolis with natural gas. Galactics natural gaswells and distribution system are powered by your electricity. The following graphic shows theflow of total monthly product output for each energy company (in $ millions) to its consumersand to each other.FreestatePower & Light(Output = a)0.8bWhat does each companys monthly output(in $ millions) have to be to satisfy bothconsumer and inter-industry demand?Create a system of linear equations to solvefor monthly outputs a and b and solve theresulting system of linear equations youcreate using substitution, elimination byaddition, or augmented matrix methods(your choice). Be sure to show your work!Galactic Gas(Output = b)0.6a710MegalopolisConsumers0Output a: $ _________ million per month******Output b: $ ___________ million per month**2*****4. Graph the inequality 4 + < 8 & show the solution set (Use following grid, if desired)yx.5. Graph the inequality 10 3 21 & show the solution set (Use following grid, if desired)3yx6. Youre the chief financial officer for Amalgamated Fitness, a local gym. You can spend nomore than $36,000 this year on new fitness equipment. For $6000 per unit, you can buyApocalyptic Fitness Supplys SpineCrusher unstoppable elliptical trainer. For $4000 per unit,you can buy Armageddon Athletic Companys Sayonara rocket-propelled free-weight set.How many SpineCrusher units and Sayonara units can you buy without exceeding budget?a. Express the answer as a linear inequalityAnswer:__________________________________b. Draw its graph, showing the solution region (Use following grid, if desired)4yx7. Solve the system graphically (use grid below if desired), show the solution region, and statethe coordinates (in ordered pair format) of each corner point:3 + 3 242 4005yx8. Solve the system graphically (use grid below if desired), show the solution region, and statethe coordinates (in ordered pair format) of each corner point:+ 42 + 6006yx9. Youre the chief financial officer at Cambridge Metal Works, which manufactures two sizesof gears. The smaller gear requires 4 hours of machining and 1 hour of polishing. The largergear requires 1 hour of machining and 1 hour of polishing. To hold down labor costs, you decidethat the firm has a MAXIMUM of 24 hours per day for machining and 9 hours per day forpolishing. Let x represent the number of smaller gears produced and y represent the number oflarger gears produced.a. Write a system of linear inequalities indicating appropriate restraints on x and yb. Find the set of feasible solutions graphically for the number of smaller gears and of largergears that can be produced in a day. Use grid below if desired. Be sure to label cornerpoints (in ordered pair format), if any exist!7yx10. An augmented matrix Q is defined as follows:= [4 67|]2 33.5a. What single row operation (e.g., 32 + 1 1 ) must be performed on Q to get thefollowing result:[1 1.51.75|]233.5b. What single row operation (e.g., 32 + 1 1 ) must be performed on Q to get thefollowing result:[4 67|]000