Assignment 3 - Linear Programming
1. Asset Allocation
A portfolio manager has $70 million to invest in the following
assets:
| Asset |
Rate of Return |
Risk |
| Growth Stocks |
14.25% |
(a) |
| Value Stocks |
8.75% |
(b) |
| Foreign Stocks |
11.25% |
(c) |
| Fixed Income (Bonds) |
7.75% |
30 |
| Cash |
4.45% |
0 |
where risk is measured on a scale from 0 - 100, with 100 being the
riskiest. The manager wants the maximum the return on the money,
subject to the following conditions:
- At least $5 million is available in cash for
emergencies/opportunities
- No more than 80% of the money can be invested in stocks
- At least 10% of the money invested in stocks should be invested
in foreign stocks
- The average risk should not exceed 50
a. How should the money be allocated?
b. What is the total return on the $70 million invested?
c. Do a complete sensitivity analysis of your results.
2. Employee Scheduling
A restaurant wants to schedule its employees in the most efficient
(least costly) way. It has determined that it needs the following
number of workers at different times of the day:
| Time |
Workers |
| 6 AM - 8 AM |
10 |
| 8 AM - 10 AM |
8 |
| 10 AM - 12 PM |
15 |
| 12 PM - 2 PM |
(d) |
| 2 PM - 4 PM |
10 |
| 4 PM - 6 PM |
(e) |
| 6 PM - 8 PM |
(f) |
| 8 PM - 10 PM |
8 |
In addition to having enough people at the different times of the
day, the restaurant also needs to meet the following requirements:
- At least two full-time employees must be on duty when the
restaurant opens at 6 AM
- At least two full-time employees must be on duty when the
restaurant closes at 10 PM
- At least four full-time employees must be on duty during the
lunch period (12 PM - 2 PM).
- At least six full-time employees must be on duty during the
dinner period (6 PM - 8 PM).
The restaurant operates with seven different shifts:
| Shift |
Type |
Daily Wages |
| 6 AM - 10 AM |
Part-time |
$25 |
| 6 AM - 2 PM |
Full-time |
$52 |
| 10 AM - 2 PM |
Part-time |
$22 |
| 10 AM - 6 PM |
Full-time |
$54 |
| 2 PM - 6 PM |
Part-time |
$24 |
| 2 PM - 10 PM |
Full-time |
$55 |
| 6 PM - 10 PM |
Part-time |
$23 |
a. How many workers should be hired for each shift?
b. What is the restaurants total wage bill?
c. What periods, if any, have excess (slack) employees, and how
much is that excess?
3. Transportation
The table below shows the travel costs between a firm’s two
production facilities (P1, P2) and its four markets (M1, M2, M3, M4):
|
|
M1 |
M2 |
M3 |
M4 |
|
P1 |
16 |
17 |
20 |
15 |
|
P2 |
18 |
15 |
15 |
14 |
P1 can produce 40 units of the firm’s product, while P2 can
produce 45 units. The demands in the four markets are 20, 16, (g), and
(h), respectively.
a. How much should the firm send from each production facility
to each of the markets?
b. What is the total transportation cost?
c. Give an interpretation of each calculated shadow price in
this situation.
4. Advertising Mix
A company is thinking of advertising on some of the new dramatic
series that the networks have introduced this season. The table below
indicates the show, the network, the overall audience rating, the
audience of 18-49 year olds, and the cost of buying a 30-second
commercial (in thousands of dollars):
|
Show |
Network |
Overall |
18-49 |
Commercial |
|
Karen Sisco |
ABC |
5.5 |
2.6 |
$134 |
|
Threat Matrix |
ABC |
4.6 |
2.0 |
$108 |
|
Joan of Arcadia |
CBS |
7.6 |
(i) |
$165 |
|
Navy NCIS |
CBS |
8.5 |
(j) |
$169 |
|
Miss Match |
NBC |
4.7 |
2.2 |
$114 |
|
Las Vegas |
NBC |
7.5 |
4.8 |
$214 |
The company wants to appeal to 18-49 year olds, and wants to buy
commercials that would allow it to reach as many of that category as
possible, subject to the following constraints:
- The advertising budget is $5,000 (000).
- It wants the overall average viewership to be at least 6.0.
- It doesn’t want any one network to have more than 45% of its
commercials.
a. What is the optimal distribution of the firm’s commercials?
b. How many gross ratings points for the 18-49 year olds will the
firm reach with its commercials?
c. Does the firm have any excess money left?
Final Output
Please submit a copy of
your analysis along with supporting computer output by Tuesday,
December 9. If the output is a hard copy, it should be
typed on 8 ½ x 11 or A4 paper. Please do not submit the
report in a special report cover; a stable in the upper
left hand corner would be adequate. The output may also
be submitted as an e-mail attachment.
| Name |
(a) |
(b) |
(c) |
(d) |
(e) |
(f) |
(g) |
(h) |
(i) |
(j) |
| Albano |
90 |
40 |
70 |
19 |
15 |
23 |
16 |
17 |
3.2 |
3.3 |
| Alipour |
90 |
40 |
75 |
19 |
15 |
22 |
16 |
18 |
3.2 |
3.1 |
| Arendale |
90 |
40 |
80 |
19 |
15 |
21 |
16 |
19 |
3.2 |
2.9 |
| Austin |
90 |
40 |
85 |
19 |
15 |
20 |
16 |
20 |
3.2 |
2.7 |
| Barrios |
90 |
40 |
90 |
19 |
15 |
19 |
16 |
21 |
3.2 |
2.5 |
| Boyer |
90 |
45 |
70 |
19 |
15 |
18 |
16 |
22 |
3.2 |
2.3 |
| Bui |
90 |
45 |
75 |
19 |
16 |
23 |
16 |
23 |
3.2 |
2.1 |
| Cardoza |
90 |
45 |
80 |
19 |
16 |
22 |
16 |
24 |
3.1 |
3.3 |
| Carlson |
90 |
45 |
85 |
19 |
16 |
21 |
16 |
25 |
3.1 |
3.1 |
| Cervantes |
90 |
45 |
90 |
19 |
16 |
20 |
16 |
26 |
3.1 |
2.9 |
| Chavez |
90 |
50 |
70 |
19 |
16 |
19 |
17 |
17 |
3.1 |
2.7 |
| Chen, Leo |
90 |
50 |
75 |
19 |
16 |
18 |
17 |
18 |
3.1 |
2.5 |
| Chen, Tia |
90 |
50 |
80 |
19 |
17 |
23 |
17 |
19 |
3.1 |
2.3 |
| Clegg |
90 |
50 |
85 |
19 |
17 |
22 |
17 |
20 |
3.1 |
2.1 |
| Coleman |
90 |
50 |
90 |
19 |
17 |
21 |
17 |
21 |
3.0 |
3.3 |
| Creighton |
90 |
55 |
70 |
19 |
17 |
20 |
17 |
22 |
3.0 |
3.1 |
| Cugini |
90 |
55 |
75 |
19 |
17 |
19 |
17 |
23 |
3.0 |
2.9 |
| Curry |
90 |
55 |
80 |
19 |
17 |
18 |
17 |
24 |
3.0 |
2.7 |
| Dabrowski |
90 |
55 |
85 |
20 |
15 |
23 |
17 |
25 |
3.0 |
2.5 |
| Diodosio |
90 |
55 |
90 |
20 |
15 |
22 |
17 |
26 |
3.0 |
2.3 |
| Dorsey |
85 |
40 |
70 |
20 |
15 |
21 |
18 |
17 |
3.0 |
2.1 |
| Felke |
85 |
40 |
75 |
20 |
15 |
20 |
18 |
18 |
2.9 |
3.3 |
| Fenske |
85 |
40 |
80 |
20 |
15 |
19 |
18 |
19 |
2.9 |
3.1 |
| Fernandez |
85 |
40 |
85 |
20 |
15 |
18 |
18 |
20 |
2.9 |
2.9 |
| Finn |
85 |
40 |
90 |
20 |
16 |
23 |
18 |
21 |
2.9 |
2.7 |
| Flores |
85 |
45 |
70 |
20 |
16 |
22 |
18 |
22 |
2.9 |
2.5 |
| Foerder |
85 |
45 |
75 |
20 |
16 |
21 |
18 |
23 |
2.9 |
2.3 |
| Fullerton |
85 |
45 |
80 |
20 |
16 |
20 |
18 |
24 |
2.9 |
2.1 |
| Geldern |
85 |
45 |
85 |
20 |
16 |
19 |
18 |
25 |
2.8 |
3.3 |
| Gerhardt |
85 |
45 |
90 |
20 |
16 |
18 |
18 |
26 |
2.8 |
3.1 |
| Gillen |
85 |
50 |
70 |
20 |
17 |
23 |
19 |
17 |
2.8 |
2.9 |
| Gleason |
85 |
50 |
75 |
20 |
17 |
22 |
19 |
18 |
2.8 |
2.7 |
| Grau |
85 |
50 |
80 |
20 |
17 |
21 |
19 |
19 |
2.8 |
2.5 |
| Gupta |
85 |
50 |
85 |
20 |
17 |
20 |
19 |
20 |
2.8 |
2.3 |
| Gutierrez |
85 |
50 |
90 |
20 |
17 |
19 |
19 |
21 |
2.8 |
2.1 |
| Hawkins |
85 |
55 |
70 |
20 |
17 |
18 |
19 |
22 |
2.7 |
3.3 |
| Huang |
85 |
55 |
75 |
21 |
15 |
23 |
19 |
23 |
2.7 |
3.1 |
| Huszar |
85 |
55 |
80 |
21 |
15 |
22 |
19 |
24 |
2.7 |
2.9 |
| Jimenez |
85 |
55 |
85 |
21 |
15 |
21 |
19 |
25 |
2.7 |
2.7 |
| Kaloti |
85 |
55 |
90 |
21 |
15 |
20 |
19 |
26 |
2.7 |
2.5 |
| Kim |
80 |
40 |
70 |
21 |
15 |
19 |
20 |
17 |
2.7 |
2.3 |
| Lalinde |
80 |
40 |
75 |
21 |
15 |
18 |
20 |
18 |
2.7 |
2.1 |
| Lanjewar |
80 |
40 |
80 |
21 |
16 |
23 |
20 |
19 |
2.6 |
3.3 |
| Lee |
80 |
40 |
85 |
21 |
16 |
22 |
20 |
20 |
2.6 |
3.1 |
| Leibham |
80 |
40 |
90 |
21 |
16 |
21 |
20 |
21 |
2.6 |
2.9 |
| Levy |
80 |
45 |
70 |
21 |
16 |
20 |
20 |
22 |
2.6 |
2.7 |
| Meiners |
80 |
45 |
75 |
21 |
16 |
19 |
20 |
23 |
2.6 |
2.5 |
| Morga |
80 |
45 |
80 |
21 |
16 |
18 |
20 |
24 |
2.6 |
2.3 |
| Nunes |
80 |
45 |
85 |
21 |
17 |
23 |
20 |
25 |
2.6 |
2.1 |
| O'Donnell |
80 |
45 |
90 |
21 |
17 |
22 |
20 |
26 |
2.5 |
3.3 |
| Osborne |
80 |
50 |
70 |
21 |
17 |
21 |
21 |
17 |
2.5 |
3.1 |
| Otani |
80 |
50 |
75 |
21 |
17 |
20 |
21 |
18 |
2.5 |
2.9 |
| Patel, Pramesh |
80 |
50 |
80 |
21 |
17 |
19 |
21 |
19 |
2.5 |
2.7 |
| Patel, Roshni |
80 |
50 |
85 |
21 |
17 |
18 |
21 |
20 |
2.5 |
2.5 |
| Peyre |
80 |
50 |
90 |
22 |
15 |
23 |
21 |
21 |
2.5 |
2.3 |
| Richardson |
80 |
55 |
70 |
22 |
15 |
22 |
21 |
22 |
2.5 |
2.1 |
| Ruiz |
80 |
55 |
75 |
22 |
15 |
21 |
21 |
23 |
2.4 |
3.3 |
| Sevick |
80 |
55 |
80 |
22 |
15 |
20 |
21 |
24 |
2.4 |
3.1 |
| Shah |
80 |
55 |
85 |
22 |
15 |
19 |
21 |
25 |
2.4 |
2.9 |
| Smith |
80 |
55 |
90 |
22 |
15 |
18 |
21 |
26 |
2.4 |
2.7 |
| Sorenson |
75 |
40 |
70 |
22 |
16 |
23 |
22 |
17 |
2.4 |
2.5 |
| Stearrett |
75 |
40 |
75 |
22 |
16 |
22 |
22 |
18 |
2.4 |
2.3 |
| Tanz |
75 |
40 |
80 |
22 |
16 |
21 |
22 |
19 |
2.4 |
2.1 |
| Tatarian |
75 |
40 |
85 |
22 |
16 |
20 |
22 |
20 |
2.3 |
3.3 |
| Tchang |
75 |
40 |
90 |
22 |
16 |
19 |
22 |
21 |
2.3 |
3.1 |
| Vanderhoof |
75 |
45 |
70 |
22 |
16 |
18 |
22 |
22 |
2.3 |
2.9 |
| Villani |
75 |
45 |
75 |
22 |
17 |
23 |
22 |
23 |
2.3 |
2.7 |
| Wang |
75 |
45 |
80 |
22 |
17 |
22 |
22 |
24 |
2.3 |
2.5 |
| Weller |
75 |
45 |
85 |
22 |
17 |
21 |
22 |
25 |
2.3 |
2.3 |
| Zachry |
75 |
45 |
90 |
22 |
17 |
20 |
22 |
26 |
2.3 |
2.1 |
|
