Name:
Math 1090-007
Midterm 1
October 1, 2010
• The use of scientific calculators is permitted for this exam.
• No notes, books, other study materials or graphing calculators are allowed.
• Each problem is worth 20 points. Do every problem for full credit.
1. Tom is four years older than Yvon. Warren is six years younger than twice Yvon’s age.
The sum of Warren’s and Yvon’s ages is six years more than twice Tom’s age. How
old is Warren?
1
2. Let A =
4 −6 7
1 3 0


−2 12
0 . Compute 3A + 2B T .
and B =  8
−7 −3
2
3. (a) Find the slope and y-intercept of the line 2y − 4x − 2 = y − 3.
(b) Write the equation of the line that passes through the point (-15,7) and is perpendicular to the line given in part (a).
(c) Find the point at which the lines from parts (a) and (b) intersect.
(d) Graph both lines.
10
y
K10
5
K5
0
5
x
K5
K10
3
10
4. My uncle Arno grows pumpkins and corn on his 90 acre farm. He makes $1000 for
every acre of pumpkins he plants and only $400 for each acre of corn. To maintain
soil quality, he cannot use more than a third of his land each year for pumpkins. He
also has a contract to grow at least 40 acres of corn to sell to a local rancher for feed.
How many acres of pumpkins and how many acres of corn should he plant each year
to maximize his profits? (Use the axes provided to graph the feasible region.)
100
80
60
corn
40
20
0
20
40
4
pumpkins
60
80
100


−3 15 34
5. Let M =  1 −5 −11 . Compute M −1 . Check your answer.
0
1
2
5
6. It costs a small record company $5,400 to record a studio album. They are able to
make CDs at a cost of only 99 cents each, but sell them to retail distributors for $9.99
each.
(a) What is the Cost function for making this record? What is the Revenue function?
(b) What is the Profit function?
(c) How many CDs must they sell in order to break even?
(d) How much profit will they make if they sell a thousand CDs?
6