Math 94
Practice Exam 4
No notes or phones are allowed. You can use a calculator. Please show all your work on this paper.
Simplify each answer fully. Each problem is worth 2 points unless otherwise specified. Good luck!
Deduction for work done in pen or for work that is hard to follow:_______ (up to 2 points)
1) Solve the following system by Cramer's Rule.
Solution: (
,
)
2) [Set up only!] Cool Cat Coffee sells 8-oz cups of coffee for $1.75, 12-oz cups of coffee for $2.30, and
16-oz cups of coffee for $2.65. During a certain period, they sold 80 cups of coffee for a total of $181.35.
The total amount of coffee sold was 980 oz. You want to find how many cups of each type they sold.
i) Clearly label 3 variables.
ii) Set up 3 equations involving the variables you labeled in (i).
3) Use row-equivalent operations to transform the following matrix into row-echelon form. You do not
have to solve.
4) Translate the following matrix into a system of equations and solve. Use
and as your variables.
5) Surfin’ Safari produces sandals. The cost to produce x sandals is
. The revenue
from producing and selling x sandals is
. How many sandals must the company produce and
sell in order to break even? Round your answer to the nearest integer. Include your units!
6) Using the information from (5) above, find the profit (or loss) from the production and sale of 30,000
sandals.
7) Orange, Inc sells uPods. If each uPod costs p dollars, consumers will demand
million uPods and the company will supply
million uPods. Find the equilibrium point.
Round to the nearest million units.
The equilibrium price is $_________ and the equilibrium quantity is __________ million uPods.