solutions_ch2.pdf - Math 308 Discussion Problems#2(Sections...

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Mathematical Applications for the Management, Life, and Social Sciences
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Chapter 10 / Exercise 1
Mathematical Applications for the Management, Life, and Social Sciences
Harshbarger
Expert Verified
Math 308 Discussion Problems #2 (Sections 2.1-2.3) – SOLUTIONS (1) When Jake works from ~ h ome, he typically spends 40 minutes of each hour on research, and 10 on teaching, and drinks half a cup of coffee. (The remaining time is spent on the internet.) For each hour he works in the math ~ d epartment, he spends around 20 minutes on research and 30 on teaching, and doesn’t drink any coffee. Lastly, if he works at a ~ c offeeshop for an hour, he spends 25 minutes each on research and teaching, and drinks a cup of coffee. ( Note: be careful about units of minutes versus hours.) (a) Last week, Jake spent 10 hours working from home, 15 hours working in his office in Padelford Hall, and 2 hours working at Cafe Allegro. Compute what was accomplished, and express the result as a vector equation.
(b) This week, Jake has 15 hours of research to work on and 10 hours of work related to teaching. He also wants 11 cups of coffee, because... of... very important reasons. How much time should he spend working from home, from his office, and from the coffeeshop?
(c) Describe the situation in part (b) as a vector equation and a matrix equation A ~ t = ~w . What do the vectors ~ t and ~w mean in this context? For which other vectors ~w does the equation A ~ t = ~w have a solution?
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Mathematical Applications for the Management, Life, and Social Sciences
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Chapter 10 / Exercise 1
Mathematical Applications for the Management, Life, and Social Sciences
Harshbarger
Expert Verified
of times at home, at the office, and at the coffeeshop, to accomplish any combination of work and coffee. But in practice there’s an important caveat: negative amounts of time don’t make sense! So we would also need impose the inequalities t 1 , t 2 , t 3 0. We haven’t learned how to do this, but the techniques exist (called linear programming ) and are important for optimization.

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