MATH 132 - Exam 2 Review - sites.csn.edu

MATH 132 - Exam 2 Review
All material covered in class is eligible for exam, this review is not all inclusive.

1. Suppose that the supply and demand for printed baseball caps are:
Supply equation p = 0.4q + 3.2
Demand equation p = −1.9q + 17
where p is the price in dollars and q is the quantity in hundreds.

(a) Find the equilibrium price and quantity
(b) Find the supply and demand (to the nearest unit) if baseball caps are

$4 each.

2. Suppose that the supply and demand for a product are:
Supply equation p = 0.2q + 3.6
Demand equation p = −0.15q + 6.925
where p is the price in dollars and q is the quantity in thousands.
Find the equilibrium price and quantity.

3. Labor costs for a farmer are $55 per acre for corn and $45 per acre for
soybeans. How many acres of each crop should the farmer plant if he wants
to spend no more than $5,000 on seed?

4. Use the system of linear inequalities to answer the question.
5x + y ≤ 32
7x + 4y ≥ 45
x, y ≥ 0

(a) Is the point (5,3) in the solution region?
(b) Is the point (5,2) in the solution region?

5. Find the coordinates of the corner points of the feasible set.
6x + 3y ≤ 24
3x + 6y ≤ 30
x, y ≥ 0

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6. A furniture manufacturing company manufactures dining-room tables and
chairs. A table requires 8 labor-hours for assembling and 2 labor-hours for
finishing. A chair requires 2 labor-hours for assembling and 1 labor-hour for
finishing. The maximum labor-hours available per day for assembling and
finishing are 400 and 120, respectively. If x is the number of tables and y is
the number of chairs produced per day, write a system of inequalities that
indicates appropriate restraints on x and y. Find the coordinates of each
corner point.

7. A particular feasible area has corner points (3,6), (6,4), (0,5), and (4,1).
Maximize and minimize the function 5x + 9y over this region.

8. Maximize P = 6x + 6y, subject to:
2x + y ≤ 30
x + 2y ≤ 24
x, y ≥ 0

9. A car rental agency has facilities at both JFK and LaGuardia airports.
Assume that a car rented at either airport must be returned to one or the
other airport. If a car is rented at LaGuardia, the probability that it will be
returned there is 0.8; if a car is rented at JFK, the probability that it will
be returned there is 0.7. Assume that the company rents all its 1,000 cars
each day and that each car is rented (and returned) only once a day. If we
start with 500 cars at each airport, then what is the expected distribution
of cars the next day? What is the expected distribution of cars 2 days later?

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10. A midwestern university offers its employees three choices for health care: a
clinic-based health maintenance organization (HMO), a preferred provider
organization (PPO), and a traditional fee-for-service program (FFS). Each
year, the university designates an open enrollment period during which em-
ployees may change from one health plan to another. Prior to the last open
enrollment period 20% of employees were enrolled in the HMO, 25% in the
PPO, and the remainder in the FFS. During the open enrollment period,
15% of employees in the HMO switched to the PPO and 5% switched to the
FFS; 20% of the employees in the PPO switched to the HMO and 10% to the
FFS; and 25% of the employees in the FFS switched to the HMO and 30%
switched to the PPO. What percentage of employees were enrolled in each
health plan after the last open enrollment period? Answer in percentage
form with 2 decimal places.

11. The two major computer operating systems are Apple’s OS and Windows.
Suppose that at this moment 40% of computers in use are Apple and 60%
use Windows. Suppose that consumers buy a new computer every 3 years
and when they do 70% of Apple users buy another Apple computer and the
remaining 30% switch to a Windows based computer. At the same time
suppose that only 40% of Windows users buy another Windows based PC.
Find the market share for each system after 3 years and after 6 years.

12. A group of physical fitness devotees works out in the gym every day. The
workouts vary from strenuous to moderate to light. When their exercise
routine was recorded, the following observation was made: of the people who
work out strenuously on a particular day, 40% will work out strenuously the
next day, 30% will work out moderately, and 30% will work out lightly. Of
those who work out moderately, 50% will work out strenuously and 50% will
work out lightly the next day. Of the people who work out lightly, 30% will
work out strenuously, 50% will work out moderately, and 20% will work out
lightly. Suppose that on a particular Monday 30% have a strenuous workout,
20% have a moderate workout, and 50% have a light workout. What percent
will have strenuous, moderate, and light workouts on Tuesday?

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13. Suppose that 60% of people who own a GM (General Motors) car buy a
GM car as their next car and 90% of people who own a non-GM car buy a
non-GM car as their next car. Assume that car owners buy a new car every
5 years and that currently 40% of the cars in the world are made by GM
(their market share is 40%). What will GM’s market share be in 5 years
and in 10 years?

14. Construct a truth table for the proposition: p ∧ (p → q)
15. Construct a truth table for the proposition: q → (p ∨ ¬ q)
16. Construct a truth table for the proposition: ¬p → (¬p ∧ q)
17. Construct a truth table for the proposition: p ∧ (¬q ∨ p)

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