1. A medical device company is allocating next year's budget among its divisions. As a result, the R&D Division needs to determine which research and development projects to fund. Each project requires various software and hardware and consulting expenses, along with internal human resources.
A budget allocation of $1,300,000 has been approved, and 35 engineers are available to work on the projects. The R&D group has determined that at most one of projects 1 and 2 should be pursued, and that if project 4 is chosen, then project 2 must also be chosen. Develop a model to select the best projects within the budgets.
| Project |
NPV |
Internal Engineers |
Additional Costs |
| 1 |
$600,000 |
9 |
$196,000 |
| 2 |
680,000 |
12 |
400,000 |
| 3 |
550,000 |
7 |
70,000 |
| 4 |
400,000 |
4 |
180,000 |
| 5 |
350,000 |
8 |
225,000 |
| 6 |
725,000 |
10 |
275,000 |
| 7 |
340,000 |
8 |
130,000 |
2. Soapbox is a local band that plays classic and contemporary rock. The band members charge $600 for a three-hour gig. They would like to play at least 30 gigs per year but need to determine the best way to promote themselves. The most they are willing to spend on promotion is $2,500. The possible promotion options are as follows:
Playing free gigs
Making a demo CD
Hiring an agent
Handing out fliers
Creating a Web site
Each free gig costs them about $250 for travel and equipment, but generates about 3 paying gigs. A high-quality studio demo CD should help the band book about 20 gigs, but will cost about $1,000.
A demo CD made on home recording equipment will cost only $400 but may result in only 10 bookings. A good agent will get the band about 15 gigs, but will change $1,500.
The band can create a Web site for $400 and would expect to generate 6 gigs from this exposure. They also estimate that they may book 1 gig for every 500 fliers they hand out, which would cost $0.80 each. They don't want to play more than 10 free gigs or send out more than 2,500 fliers.
Develop an solve an optimization model to find the best promotion strategy to maximize their revenue.
3. Anya is a part-time MBA student who works full time and is constantly on the run.
She recognized the challenge of eating a balanced diet and wants to minimize cost while meeting some basic nutritional requirements. Based on some research, she found that a very active woman should consume 2,250 calories per day. According to one author's guidelines, the following daily nutritional requirements are recommended:
| Source |
Recommended Intake (grams) |
| Fat |
maximum 75 |
| Carbohydrates |
maximum 225 |
| Fiber |
maximum 30 |
| Protein |
at least 168.75 |
She chose a sample of meals that could be obtained from healthier quick-service restaurants around town as well as some that could be purchased at the grocery store.
| Food |
Cost/Serving |
Calories |
Fat |
Carbs |
Fiber |
Protein |
| Turkey sandwich |
$4.69 |
530 |
14 |
73 |
4 |
28 |
| Baked potato soup |
$3.39 |
260 |
16 |
23 |
1 |
6 |
| Whole grain chicken sandwich |
$6.39 |
750 |
28 |
83 |
10 |
44 |
| Bacon turkey sandwich |
$5.99 |
770 |
28 |
84 |
5 |
47 |
| Southwestern refrigerated chicken wrap |
$3.69 |
220 |
8 |
29 |
15 |
21 |
| Sesame chicken refrigerated chicken wrap |
$3.69 |
250 |
10 |
26 |
15 |
26 |
| Yogurt |
$0.75 |
110 |
2 |
19 |
0 |
5 |
| Raisin bran with skim milk |
$0.40 |
270 |
1 |
58 |
8 |
12 |
| Ceral bar |
$0.43 |
110 |
2 |
22 |
0 |
1 |
| 1 cup of broccoli |
$0.50 |
25 |
0.3 |
4.6 |
2.6 |
2.6 |
| 1 cup of carrots |
$0.50 |
55 |
0.25 |
13 |
3.8 |
1.3 |
| 1 scoop protein powder |
$1.29 |
120 |
4 |
5 |
0 |
17 |
Anya does not want to eat the same entrée (first six foods) more than once each day but doe not mind eating breakfast or side items (last five foods) twice a day and protein powder-based drinks up
to four times a day for convenience. Develop an integer linear optimization model to find the number of servings of each food choice in a daily diet to minimize cost and meet the nutritional targets.