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Name your file using 3 fields:

Yourlastname Yourfirstname

MGSC1205A5

Submissions must be a SINGLE

SCANNED

PDF file (Please note that my solutions are 10 pages and 196

KB

.

MGSC 1205 W21 A5
Name (print):
__________________________
Student A#:
Section:
SOLUTIONS TOTAL marks = 14 + 12 + 12 + 10 + 7 = 55
__________________________
__________________________
Due Date & Time:
Wednesday Apr 7, 2021
by 1:00 p.m.
INSTRUCTIONS:
1. Name your file using 3 fields: Yourlastname Yourfirstname MGSC1205A5
2. Submissions must be a SINGLE SCANNED PDF file (Please note that my solutions are 10
pages and 196 KB. Try to keep your submissions to around that.)
3. Your assignment may be handwritten or typed or a combination thereof.
4. Scanned submissions must be in order and easily read. Ensure that you scan square to
the image and using indirect light.
5. Ensure that you include units of measurement and a statement as well as showing your
calculations.
7. Emailed assignments will not be accepted.
8. Compliance: By submitting your work to the dropbox, you acknowledge the terms of the
Compliance statement posted on Brightspace.
1. [14 marks] An investor wishes to invest at most \$14.5 million in a diversified portfolio. The
types of investments, the associated anticipated return per year and the maximum as a
proportion (%) of the portfolio to be considered are:
Investment
Anticipated return (%) Max proportion (%)
Low-income Mortgage Loans
7.00
20
Conventional Mortgage Loans
6.25
60
8.25
25
Bond Investments
5.75
15
Stock Investments
8.75
15
9.50
12
In addition, at least 20% of the investments are to be in instruments other than mortgages.
a. [6 marks] Formulate as an LP
b. [4 marks] Solve using Solver. Provide your final tableau showing the problem set up
and the final solution.
c. [4 marks] How should the investment be diversified to make the most return?
2. [12 marks] Canada Comfort has production operations in Amherst and Trois-RiviÃƒÂ¨res.
Production capacity for these plants for one type of heat pump is at most 5,000 and 2,500 per
month, respectively. The company distributes its heat pumps through three warehouses
located in Quebec City, Mississauga, and Winnipeg. The monthly forecast of minimum
demand for the warehouses is 3,500, 1,500, and 2,000 units, respectively. The cost (in
dollars) for each unit shipped on each route are shown here:
Production
Quebec City
Amherst
25
Trois-RiviÃƒÂ¨res
26
Warehouses
Mississauga
20
21
Winnipeg
30
31
Canada Comfort wants to determine a shipping schedule to satisfy the minimum demand
for each warehouse and to minimize the shipping cost.
a. [4 marks] Formulate as an LP model.
b. [4 marks] Solve using Solver. Provide your final tableau.
c. [4 marks] What is the optimal solution.
3. [12 marks] Clean & Tidy operates seven days a week and has minimum requirements with
respect to the number of employees to be available for each day to meet the needs of their
clients. Currently, employees must all work full-time, that is, five consecutive days and two
days off, each week. The minimum number of employees required per day follows:
Day
Min. No.
Monday Tuesday
18
13
Wednesday Thursday
17
11
a. [6 marks] Formulate as an LP.
Friday
15
Saturday
16
Sunday
14
b. [2 marks] Solve using solver. Provide your final tableau.
c. [4 marks] What is the optimal solution?
4. [10 marks] Herbes de Provence produces jams, jellies and oils using their home-grown
herbs. They are planning to expand their product line to include soaps, shampoos, lotions,
and other personal care products featuring their herbs. Construction of the new facility will
cost \$450,000. The end-of-month payment schedule is provided below along with the
different start-of-month investment options for creating a sinking fund to meet the payments.
Formulate an LP to meet the required schedule while placing the least amount of money into
the sinking fund. Do NOT solve.
Payment schedule:
End of month:
1
Amount due (\$1000s) \$150
2
3
\$0 \$100
4
\$0
5
\$75
6
\$75
7
\$50
Investments available:
Investment
A
B
C
D
E
Available start of month: Months to Maturity
1
1, 3
1, 4
1, 3, 5
1, 2, 3, 4, 5, 6, 7
7
5
4
3
1
Yield at Maturity
(end of month)
10.5 %
6.1 %
5.5 %
4.7 %
3.6 %
5. [7 marks] SND uses three raw materials to produce three products: a fuel additive, a solvent
base, and a carpet cleaning fluid. The following information is provided:
Profit per ton (excl set up costs)
Set up Costs
Maximum Production (tons)
Material 1 (tons)
Material 2 (tons)
Material 3 (tons)
Products
Fuel
Solvent
Carpet
Maximum
Cleaner
Available
\$40
\$30
\$50
\$200
\$50
\$400
50
25
40
0.4
0.5
0.6
20
0.2
0.1
5
0.6
0.3
0.3
21
Formulate as a BIP to maximize net Profit of the three products. Note: Set-up costs are incurred
only if that product is produced and are not included in the Profit per ton. Do NOT solve.