BUS310 LandCos Apartment Building for Undergraduate Students Problem Sheet Please check the attached file and use the Optimization Template provided. • • Y

BUS310 LandCos Apartment Building for Undergraduate Students Problem Sheet Please check the attached file and use the Optimization Template provided. •
•
You are allowed one submission attempt.
Please note that you are required to use the Optimization Template demonstrated in class
to complete this exam.
It is extremely important that you keep all reports and answer sheets organized, all to the
right of the problem worksheet.
Problem 1:
LandCo, a real estate developer is planning to build an apartment building specifically for
undergraduate students on a parcel of land adjacent to UDC. Four types of apartments can be
included in the building: efficiencies, and one, two, and three bedroom units. Each efficiency
requires 500 square feet; each one bedroom unit requires 700 square feet; each two bedroom unit
requires 800 square feet; and each three bedroom unit requires 1,000 square feet. The developer
believes that the building should include no more than 15 one bedroom units, 22 two bedroom
units, and 10 three bedroom units. Local zoning ordinances do not allow the developer to build
more than 40 units in a particular building location, and restrict the building to a maximum of
40,000 square feet. The developer has already agreed to lease 5 one bedroom units and 8 two
bedroom units to a local rental agency. Market studies indicate that efficiencies can rent for
$350/month, one bedroom units can rent for $450/month, two bedroom units can rent for
$550/month, and three bedroom units can rent for $750/month. How many units of each type
should the developer build to maximize revenue?
Problem 2:
Highlander Technologies makes three types of smart phones: the HipI, the HipII, and the
OldGeezer. Each smart phone requires some labor, in the fabrication department, in the assembly
department, and in the shipping department. The smart phones are sold through a local dealer who
has estimated the maximum demand for the coming quarter for the HipI, the HipII, and the
OldGeezer of 300, 250, and 100 units respectively. The dealer makes profit of, $15, $24, and $18
for the HipI, the HipII, and the OldGeezer respectively. The fabrication department has a
maximum of 1850 hours for the quarter. The assembly department has a maximum of 2400 hours
for the quarter. The shipping department has a maximum of 1500 hours for the quarter. The HipI
model requires 4 hours, 3 hours, and 3 hours for fabrication, assembly, and shipping respectively.
The HipII model requires 6 hours, 5 hours, and 2 hours for fabrication, assembly, and shipping
respectively. The OldGeezer requires 2 hours, 7 hours, and 4 hours for fabrication, assembly, and
shipping respectively. The goal is to maximize profit with the best product mix. Work-in-progress
is OK.
Problem 3:
ElectroLaser Corporation makes RADAR detectors and assembles two models: the Speed King
I and the Speed King II. The firm can sell all they make in the Fairfax county. Both models use
the same components. The two main components can only be sources from one local supplier.
For the next month, the supply of component A is limited to 4,000 and the supply of component
B is limited to 3,500. Speed King I uses 18 of component A and 6 of component B. Speed King
II uses 12 of component A and 10 of component B. Speed King I has a unit profit of $24, and
Speed King II has a unit profit of $40. How many of each model should the company make to
maximize profit?
Problem 4:
DC Manufacturing produces two types of academic desks, standard and deluxe. Deluxe desks
have oak tops and more expensive hardware and require additional time for finishing and
polishing. Standard desks require 70 board feet of pine, and 10 hours of labor. The deluxe desk
requires 60 board feet of pine, 18 board feet of oak and 15 hours of labor. For the next week, the
DC Manufacturing has 5,000 board feet of pine, 750 board feet of oak, and 400 hours of labor.
Standard desk has a net profit of $225 and the deluxe desk has a net profit of $320. The company
must make at least 3 deluxe desks. How many of each type of desk should the company make to
maximize profit for the next week?
Problem 5:
Crozet Outside Products (COPs, Inc.) produces three kinds of hand crafted outdoor, ultralightweight, totally hip chairs: sling chairs, Adirondack chairs and hammocks. The unit profit for
each of these products is $35.00, $75.00 and $100, respectively. Each type of chair requires
cutting, assembly, and finishing time. The owner is retired, but she is willing to work 120 hours
per month. She does not want to work more than 50 hours per month doing any one of the specific
activities, cutting, assembly or finishing. These chairs are very popular in Crozet, so as usual she
can sell all she makes. Sling chairs require 30 minutes for cutting, assembly requires 45 minutes,
and finishing takes 1 hour. Adirondack chairs take 2 hours for both cutting and assembly and 1
hour for finishing. The very popular hammock model requires 24 minutes for cutting, 3 hours to
assemble, and 1 hour to finish. How many of each chair should the owner make to maximize
profit? (hint: sum the time to produce each chair type, use the values as coefficients for a
constraint. Be careful with units… need all be the same)
Problem 6:
DC Milling grinds calcined alumina to a standard granular size. The mill produces two different
size products from the same raw material. Regular Grind can be produced at a rate of 10,000
pounds per hour and has a demand of 400 tons per week with a price per ton of $900. Super Grind
can be produced at a rate of 6,000 pounds per hour and has a demand 200 tons per week with a
price of $1,900 per ton. A minimum of 700 tons has to be ground every week to make room in the
raw material storage bins for previously purchased incoming raw material by rail. The mill
operates 24/7 for a total of 168 hours/week. How many tons of each product must be produced
each week to maximize revenue? (hint: be careful with units in this problem, ton, ton per week,
ton per hour).
Problem 7:
DC Model Cars produces four different radio-controlled model cars based on high end
production models: Ferrari, BMW, Lotus, and Tesla. Each model requires production in five
departments: molding, sanding, polishing, painting, and finishing. The required minutes in each
department is listed below. Marketing indicates that the company has to make at least 25 of each
model. How many of each model should be made to maximize profit?
Molding
Ferrari
BMW
Lotus
Tesla
Minutes Available
Sanding
5
3.5
1
3
600
4
3.2
2
3.65
600
Polishing
3.5
2
3
1
480
Painting
Finishing
3.75
4
3.25
1
1.75
2
2
3
480
480
Price
$350.00
$330.00
$270.00
$255.00
Problem 8:
Terrific Teas, Inc. markets three blends of tea: Premium, Duke Grey, and Breakfast. The firm
uses tea leaves sources from India, China, and California. The net profit per pound for each blend
is: $0.45 for Premium, $0.40 for Duke Grey, and $0.30 for Breakfast. The firm’s regular weekly
supplies are 20,000 pounds of Indian tea leaves, 22,000 pounds of Chinese tea leaves, and 16,000
pounds of California tea leaves. Determine the optimal product mix to maximize profits. Please
do not change the values in the matrix to decimals.
Tea Leaves Percent
Quality
India
China
California
Premium
40
20
40
Duke Grey
30
50
20
Breakfast
40
40
20
Problem 9:
Fairfax Furnaces, Inc. operate a power plant that includes a coal fired boiler to product steam to
drive a generator. They are aware that they need to replace the old boiler due to emission issues.
The company can purchase four different types of coal from West Virginia and blend them to meet
the requirements for burning in the boiler. The following table shows the characteristics of the
different types of coal:
Type of Coal
Type Anthracite
Type Bituminous
Type Sub-bituminous
Type Lignite
BTU/lb
% Ash
% Moisture
11,500
11,800
12,200
12,100
13
10
12
12
Cost $/lb
10
8
8
8
$2.49
$3.04
$2.99
$2.61
The required BTU/pound must be at least 11,900. In addition, the ash content can be at most
12.2% and the moisture content can be at most 9.4%. Develop an optimization model to minimize
cost which will be in cost per pound. Please do not change the percentage values in the matrix to
decimals. The total percentage of the mix, must equal 1. This is a hard problem, please take your
time!
Problem 10:
Graph the following linear inequalities on the digital graph paper worksheet Problem 10. Show
ALL your algebra steps that are required to determine the X and Y intercepts for both equations
in the text box. From the MS Excel ribbon > Insert > Shapes > Lines.
Line #
X coefficient
Y coefficient
1
2
3
3
6
1
4
3
0
“RHS”
?
?
?
36
48
7
Use the text box for you answer. Solve algebraically, showing ALL steps, for the solution, or
“intersection” of:
1. Equation 1 and equation 2.
2. Equation 1 and equation 3
3. Equation 2 and equation 3
4. What extreme points bound the feasible region? List the coordinates
If needed, show solutions in decimals, not fractions. Show the final X and Y values in BOLD.
Template!
DV1
DV2
…
Unit Profit
DVs
Max Profit
Used
C1
C2
C2
?
1. Name the decision variables:
RHS
?
?
?
2. What is the optimal values of the decision
variables:
3. What is the optimal objective function:

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