BA 452 Quantitative Analysis Final Exam

1 BA 452 Quantitative Analysis Final Exam 1 This is a 150-minute exam (2hr. 30 min.). There are 6 questions (25 minutes per question). To avoid the temptation to cheat, you must abide by these rules then sign below after you understand the rules and agree to them: Turn off your cell phones. You cannot leave the room during the exam, not even to use the restroom. The only things you can have in your possession are pens or pencils and a simple non-graphing, non-programmable, non-text calculator. All other possessions (including phones, computers, or papers) are prohibited and must be placed in the designated corner of the room.

2 Possession of any prohibited item (including phones, computers, or papers) during the exam (even if you don t use them but keep them in your pocket) earns you a zero on this exam, and you will be reported to the Academic Integrity Committee for further action. Print name here:_____ Sign name here:_____ Each individual question on the following exam is graded on a 4-point scale. After all individual questions are graded, I sum the individual scores, and then compute that total as a percentage of the total of all points possible. I then apply a standard grading scale to determine your letter grade: 90-100% A; 80-89% B; 70-79% C; 60-70% D; 0-59% F Finally, curving points may be added to letter grades for the entire class (at my discretion), and the resulting curved letter grade will be recorded on a standard 4-point numerical scale.

3 Tip: Explain your answers. And pace yourself. When there is only hour left, spend at least 5 minutes outlining an answer to each remaining question. For all of the exam, you may only use blank or graph paper, pencils, and a calculator. You may not use a computer or notes. BA 452 Quantitative Analysis Final Exam 2 Manipulating Alternatives to No Agreement Question 1. Consider negotiations over wages for adjunct Management Science Professors at the Business Administration Division of Seaver College of Pepperdine University. Pepperdine seeks a professor for the next 5 semesters. The only candidate (Charlie) is willing to work for as little as $5,000 per semester and Pepperdine is willing to pay up to $35,000 per semester.

4 Before the first semester, Pepperdine confronts the candidate Charlie over wages. Pepperdine presents its wage offer. Charlie either accepts it or rejects it and returns the next semester with a counteroffer. Offers alternate thereafter. Employment only occurs in those semesters after an agreement is reached. What wage per semester should Pepperdine offer to Charlie? Should Charlie accept that initial offer? Now suppose candidate Charlie finds an alternative employment offer by UCLA, who makes Charlie a take-it-or-leave-it offer of $15,000 for each of the same 5 semesters. Suppose the candidate cannot accept the job at both UCLA and Pepperdine University.

5 Re-compute Pepperdine s initial wage offer to Charlie. Finally suppose, in addition to the alternative employment offer to candidate Charlie by UCLA described above, the problem changes because Pepperdine finds an alternative candidate Chris who makes Pepperdine a a take-it-or-leave-it offer to work for $25,000 per semester for each of the same 5 semesters. Re-compute Pepperdine s initial wage offer to Charlie. Answer to Question: BA 452 Quantitative Analysis Final Exam 3 Answer to Question: To consider all possible wage offers (offers by Pepperdine to buy labor by the candidate to sell labor), consider a bargaining payoff table.

6 The game ends if an offer is accepted or if the semesters end without an accepted offer, and gains are measured as a percentage of the gain from the candidate accepting Pepperdine s offer before the first semester. Without the alternative offer, the candidate s opportunity cost of Pepperdine employment is $5,000 per semester, and so the gain from Pepperdine employment is $30,000=$35,000-$5,000 per semester. For Pepperdine to receive 60% of those gains, Pepperdine gains $18,000 per semester, which means offer wages $17,000=$35,000-$18,000 per semester, or $85,000 for all five semesters. And Charlie should accept that initial offer.

7 With the alternative employment offer to candidate Charlie, the candidate s opportunity cost of Pepperdine employment is $15,000 per semester, and so the gain from Pepperdine employment is $20,000=$35,000-$15,000 per semester. For Pepperdine to receive 60% of those gains, Pepperdine gains $12,000 per semester, which means offer wages $23,000=$35,000-$12,000 per semester, or $115,000 for all five semesters. And Charlie should accept that initial offer. Comment: Charlie finding alternative employment raised candidate Charlie s Pepperdine wages. Rounds t o End of GameOffer byT ot al Gain t o DivideP 's GainOfferedC's GainOffered1P202002C4020203P6040204C8040 405P1006040BA 452 Quantitative Analysis Final Exam 4 With the alternative employment offer to candidate Charlie and the alternative employment offer from candidate Chris, candidate Charlie s opportunity cost of Pepperdine employment is $15,000 per semester and Pepperdine s value to Charlie s employment is $25,000 per semester.

8 So, the gain from Pepperdine employment is $10,000=$25,000-$15,000 per semester. For Pepperdine to receive 60% of those gains, Pepperdine gains $6,000 per semester, which means offer wages $19,000=$25,000-$6,000 per semester, or $95,000 for all five semesters. And Charlie should accept that initial offer. Comment: Pepperdine finding an alternative candidate lowered candidate Charlie s Pepperdine wages. BA 452 Quantitative Analysis Final Exam 5 Sensitivity to Constants Question 2. The Ford Motor Company makes cars and trucks on an assembly line. Each car and truck requires labor and needs to visit three stations: engine installation, hood installation, and wheel installation.

9 The hours of labor and hours required at each station are as follows: There are available 12 hours of labor, 48 hours of engine installation, 20 hours of hood installation, and 12 hours of wheel installation. Labor costs $20 per hour, and each installation station costs $10 per hour to operate. Cars sell for $710 each, and trucks sell for $530 each. a. Formulate and graphically solve for the recommended production quantities. Do not require production units to be integers. b. How much should Ford be willing to pay to another potential worker (Joe) to supply one more unit of labor. (Joe is not part of the 12 hours of labor mentioned above.)

10 Answer to Question: Engine Hood Wheel Vehicle Labor Installation Installation Installation Car 4 6 4 3 Truck 3 8 5 4 BA 452 Quantitative Analysis Final Exam 6 Answer to Question: a. The profit contributions are $500 for each car, and $300 for each truck. Let C = cars produced. Let T = trucks produced. Max 500C + 300T 4C + 3T < 12 (labor) 6C + 8T < 48 (engine) 4C + 5T < 20 (hood) 3C + 4T < 12 (wheel) C, T 0 A graph of the feasible set shows the engine and hood constraints are redundant, and the iso-value lines show the optimal solution occurs where the labor constraint and the non-negativity of T bind (C = 3 and T = 0).