Classroom Fun Math 125, Elementary Linear Algebra, Fall 2017 Problem 1.(1 Bonus Point.) You are a manager at the Canadian government's top secret Department K. It's your task to hire some new employees for the Weapon X project. There are two types of people you need to hire, miners and scientists, but they will share duties. Miners are able to spend 2 hours a day mining precious adamantium metal from a nearby mountain plus 1 hour a day doing lab work. Since they aren't around the office for too long you only need to provide miners with 1 meal a day. Scientists can spend 1 hour a day mining plus 4 hours a day doing lab work. You will need to provide them with 3 meals a day to do this. Department K needs the new hires to (collectively) mine for at least 11 hours a day and (collectively) do lab work for at least 16 hours a day. The cook at Department K can only prepare at most 18 extra meals a day. You must pay miners $700 a day and scientists $400. You can hire at most 10 people. How many miners do you hire and how many scientists if you want to minimize the amount you spend on them? Problem 2.(1 Bonus Point.) A pension fund has $30 to invest divided among Treasury notes, bonds, and stocks. Rules for the administration of the fund require that at least $3 million go into each type of investment, at least half into Treasury notes and bonds, and the amount of bonds cannot exceed twice the amount invested in Treasury notes. The annual yields are 3% for Treasury notes, 4% for bonds, 6% for stocks. How should the money be allocated to maximize returns? Problem 3.(1 Bonus Point.) A Maryland TV dealer has stores in Annapolis and Rockville and warehouses in College Park and Baltimore. The cost of shipping a TV from College Park to Annapolis is $6. The cost of shipping a TV from College Park to Rockville is $3. The cost of shipping a TV from Baltimore to Annapolis is $8. The cost of shipping a TV from Baltimore to Rockville is $5. The Annapolis store orders 25 TVs. The Rockville store orders 30 TVs. The College Park warehouse has 45 TVs. The Baltimore warehouse has 40 TVs. How many TVs should each warehouse ship to each store to satisfy these orders and minimize costs