Self-exercises
1. Suppose the only foods in the world are as follows:
Food
Energy
Protein
Calcium Price
Types
(Kcal)
(g)
(mg)
Oatmeal
110
4
2
3
4
Chicken
205
32
12
24
3
Eggs
160
13
54
13
2
Whole Milk
160
8
285
9
8
Cherry Pie
120
4
22
20
2
Pork & Beans
260
14
80
19
2
(cents/serving)
Limit
servings/day
 A satisfactory diet has at least 2000 kcal of energy, 55g of protein, and 800 mg of calcium.
Formulate this problem as LPP to find out the least cost diet?
2. The Mid Town Food store stocks mangoes during early summer season. These are flown-in from
nearby Island, Gondar, each Monday and just be sold within the week following.
In the past, the store has been experiencing the following sales of mangoes:
Quantities Buyers Bought
# of weeks this occurred
20
10
25
30
40
50
60
10
Food Store buys mangoes for $2 and sells them for $4.
Required:
Given this, apply each of the following criteria to determine the optimal quantity of mangoes that must
be stocked per week:
A. Expected Value Criterion (EMV)
B. Criterion of Maximum Likelihood (use the maximum likelihood)
1|Page
C. Criterion of Rationality (assign equal probabilities for each states of nature)
3. Suppose that you are the sales manager of one of the supermarkets chain in Addis Abeba. You are
trying to make a decision about the optimal number of bottles of beer that should be stocked for
each month. The cost of each bottle to the supermarket is $6o and the beer is sold for a revenue of
$95 per beer. For each bottle that is unsold by the end of the week and returned back, the
supermarket receives $20.The sales data for the last 50 weeks is given as follows:
Quantities Buyers
# of weeks this occurred
Bought
20
20
21
15
22
10
23
5
Required
A. Using the Expected Value Criterion, obtain the optimal number of bottles the sales manager of
the supermarket should stock per month.
B. Using the maximum Likelihood Criterion, obtain the optimal number of bottles the sales
manager of the supermarket should stock per month
4. One of the main products of a Company is canned peas. The peas are prepared at three canneries (1,
2, & 3) and are then shipped by truck to four distributing warehouses (1,2,3,& 4). Because shipping
costs are a major expense, management has begun a study to reduce them. For the upcoming
season, an estimate has been made of what the output will be from each cannery, and how much
each warehouse will require to satisfy its customers. The shipping costs from each cannery to each
warehouse has also been determined as in the table below:
Warehouse
1
Cannery
2|Page
2
Output
3
4
1
464 513 654 867
75
2
352 416 690 791
125
3
995 682 388 685
100
Requirement
80
65
70
85
Required: Represent this problem as a LP Model
5. Formulate the following production problem as a transportation model. The demands for a given
item are 150, 250, 200 units for the next three months. The demand may be satisfied by excess
production in an earlier month held in stock for later consumption, production in the current
month, or excess production in a later month backordered for preceding months. The variable
production cost per unit in any month is $6.00. A unit produced for later consumption will incur a
storage cost at the rate of $1 per unit per month. On the other hand, backordered items incur a
penalty cost of $3.00 per unit per month. The production capacity in each of the next three months
is 200 units. The objective is to devise a minimum cost production plan.
6. The Head of the School of Management and Public Administration must plan the school’s course
offerings for the second semester. Student demands make it necessary to offer at least 30
undergraduate and 20 graduate courses in the term. Faculty contracts also dictate that at least 60
courses be offered in total. Each undergraduate course taught costs the school an average of birr
10,000 in faculty wages, and each graduate course costs birr 12,000. How many undergraduate and
graduate courses should be taught in the semester so that total faculty salaries are kept to a
minimum?
3|Page