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?

##### We have textbook solutions for you!

**The document you are viewing contains questions related to this textbook.**

**The document you are viewing contains questions related to this textbook.**

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.