bus660 midterm quantitative methods for business questions 1 30 3 in 1 test banks test bank 1 961 quanttatve methods for business midterm exam questons 1 30 3 in 1 test banks test bank 1 96
Quantitative Methods For Business
Midterm Exam: Questions 1-30 : 3 in 1 test banks
Test bank 1: 96.1%
1) Problem 7-37 (Algorithmic)
The New England Cheese Company produces two cheese spreads by blending mild cheddar
cheese with extra sharp cheddar cheese. The cheese spreads are packaged in 12-ounce containers,
which are then sold to distributors throughout the Northeast. The Regular blend contains 85%
mild cheddar and 15% extra sharp, and the Zesty blend contains 75% mild cheddar and 25%
extra sharp. This year, a local dairy cooperative offered to provide up to 9000 pounds of mild
cheddar cheese for $1.50 per pound and up to 4000 pounds of extra sharp cheddar cheese for
$1.70 per pound. The cost to blend and package the cheese spreads, excluding the cost of the
cheese, is $0.25 per container. If each container of Regular is sold for $2.00 and each container
of Zesty is sold for $2.50, how many containers of Regular and Zesty should New England
Cheese produce? Do not round your interim computations. If required, round your answers to the
nearest whole number.
Let R
number of containers of Regular
=
Z = number of containers of Zesty
Optimal Solution: R = 0, Z = 16000, profit = $ 10260.
2) A posterior probability associated with sample information is of the form
P(a state of nature | a sample outcome)
3) Problem 1-15 (Algorithmic)
Preliminary plans are underway for construction of a new stadium for a major league baseball
team. City officials question the number and profitability of the luxury corporate boxes planned
for the upper deck of the stadium. Corporations and selected individuals may purchase a box for
$300000. The fixed construction cost for the upper-deck area is estimated to be $4575000, with a
variable cost of $150000 for each box constructed.
a. What is the breakeven point for the number of luxury boxes in the new stadium?
Breakeven point 30.5 luxury boxes
b. Preliminary drawings for the stadium show that space is available for the construction of
up to 49 luxury boxes. Promoters indicate that buyers are available and that all 49 could
be sold if constructed. What is your recommendation concerning the construction of
luxury boxes?
, The input in the box below will not be graded, but may be reviewed and considered by
your instructor.
c. What profit is anticipated?
Profit $277500
4) Which of the methods for decision making best protects the decision maker from undesirable
results?
the conservative approach
5) Because the dual price represents the improvement in the value of the optimal
solution per unit increase in right-hand-side, a dual price cannot be negative.
False
6) Problem 2-11 (Algorithmic)
Let A be an event that a person's primary method of transportation to and from work is an
automobile and B be an event that a person's primary method of transportation to and from
work is a bus. Suppose that in a large city P(A) = 0.45 and P(B) = 0.34.
a. Are events A and B mutually exclusive?
Yes
What is the probability that a person uses an automobile or a bus in going to and from work? If
required, round your answer to two decimal places. 0.79
b. Find the probability that a person’s primary method of transportation is some means other
than a bus. If required, round your answer to two decimal places.
P(Bc) = 0.66
7) Problem 3-13 (Algorithmic)
Military radar and missile detection systems are designed to warn a country of enemy attacks. A
reliability question deals with the ability of the detection system to identify an attack and issue
the warning. Assume that a particular detection system has a 0.91 probability of detecting a
missile attack. Answer the following questions using the binomial probability distribution:
a. What is the probability that one detection system will detect an attack? If required, round
your answer to two decimal places. 0.91
b. If two detection systems are installed in the same area and operate independently, what is
the probability that at least one of the systems will detect the attack? If required, round
your answer to two decimal places. 0.99
, c. If 3 systems are installed, what is the probability that at least one of the systems will
detect the attack? If required, round your answer to four decimal places. 1.0000
d. Would you recommend that multiple detection systems be operated? Yes
8) Problem 8-21 (Algorithmic)
Round Tree Manor is a hotel that provides two types of rooms with three rental classes: Super
Saver, Deluxe, and Business. The profit per night for each type of room and rental class is as
follows:
Rental Class
Super Saver Deluxe Business
Type I $36 $38 —
Room
Type II $15 $26 $38
Type I rooms do not have wireless Internet access and are not available for the Business rental
class.
Round Tree's management makes a forecast of the demand by rental class for each night in the
future. A linear programming model developed to maximize profit is used to determine how
many reservations to accept for each rental class. The demand forecast for a particular night is
140 rentals in the Super Saver class, 60 rentals in the Deluxe class, and 40 rentals in the Business
class. Round Tree has 125 Type I rooms and 135 Type II rooms.
a. Use linear programming to determine how many reservations to accept in each rental
class and how the reservations should be allocated to room types.
Variable # of reservations
SuperSaver rentals allocated to room type I 125
SuperSaver rentals allocated to room type II 15
Deluxe rentals allocated to room type I 0
Deluxe rentals allocated to room type II 60
Business rentals allocated to room type II 40
Is the demand by any rental class not satisfied? No
b. How many reservations can be accommodated in each rental class?
, Rental # of
Class reservations
SuperSaver 140
Deluxe 60
Business 40
c. Management is considering offering a free breakfast to anyone upgrading from a Super
Saver reservation to Deluxe class. If the cost of the breakfast to Round Tree is $5, should
this incentive be offered?
Yes
d. With a little work, an unused office area could be converted to a rental room. If the
conversion cost is the same for both types of rooms, would you recommend converting
the office to a Type I or a Type II room? Type I
Why? Converting it to a type I room will increase the # of available rooms
e. Could the linear programming model be modified to plan for the allocation of rental
demand for the next night?
Yes
9) If P(A B) = P(A) + P(B), then A and B are mutually exclusive.
True
10) Z is a standard normal random variable. What is the value of z if the area to the right of z is
0.9803?
-2.06
11) The improvement in the value of the objective function per unit increase in a right-hand
side is the
Dual Price
12) Problem 4-05 (Algorithmic)
In American football, touchdowns are worth 6 points. After scoring a touchdown, the scoring
team may subsequently attempt to score 1 or 2 additional points. Going for 1 point is virtually an
assured success, while going for 2 points is successful only with probability p. Consider the
following game situation. The Temple Wildcats are losing by 14 points to the Killeen Tigers near
the end of regulation time. The only way for Temple to win (or tie) this game is to score two
touchdowns while not allowing Killeen to score again. The Temple coach must decide whether to
attempt a 1-point or 2-point conversion after each touchdown. If the score is tied at the end of
regulation time, the game goes into overtime. The Temple coach believes that there is a 55%
chance that Temple will win if the game goes into overtime. The probability of successfully
converting a 1-point conversion is 1.0. The probability of successfully converting a 2-point
conversion is p.
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