QUESTION B1 [15 marks] The Bloom & Blossom Company wants to expand its activitie
ID: 2924998 • Letter: Q
Question
QUESTION B1 [15 marks]
The Bloom & Blossom Company wants to expand its activities. In the next few years a number of large capital amounts will become untied, and they wish to plough these back into the company. The amounts that will become available at the beginning of each year are given in the following table:
Year
Amount
1
R150 000
2
R135 000
3
R210 000
4
R120 000
5
R 90 000
Four projects are being considered. The capital needed per year for each project (in R1 000) and the present value of the net return (in R1 000) on each project are given in the table below.
If a project is selected, it has to be completed as a whole. Money not used can be invested at 12% per annum for a year. Bloom & Blossom wants to select one or more of the projects in such a way that the net return on the chosen projects will be a maximum. Formulate the problem as linear integer programming model. Do not solve the model!
QUESTION B2 [15 marks]
(a) Give a full definition of the concept of simulation. (1)
(b) Set out the general simulation methodology in ten steps using a flow diagram. (5)
At a bakery, the daily demand for bread (in loaves) has the following probability distribution:
Demand (loaves) Probability
1 000 0,10
2 000 0,30
3 000 0,45
4 000 0,15
(c) What is the expected daily demand for bread at the bakery? (2)
(d) In a simulation run, the daily demand for bread is generated from the probability distribution by sequentially using the uniformly distributed random numbers U1, U2, : : :, as given in Appendix A.
(i) What is the demand for bread on the first day of the simulation run? (1)
(ii) What is the average demand for bread over the first four days of the simulation run? (3)
(iii) Draw a flow diagram of the logic to calculate the average daily demand for bread over
the duration of a year (365 days). (Define any variables that you use clearly) (3)
QUESTION B3 [15 Marks]
A decision maker faced with four decision alternatives and four sates of nature develops the following profit payoff table.
States of nature
Decision alternative
S_1
S_2
S_3
S_4
d_1
14
9
10
5
d_2
11
10
8
7
d_3
9
10
10
11
d_4
8
10
11
13
(a) State and use the average payoff strategy to choose the best decision. (3)
(b) State and use the aggressive strategy to choose the best decision. (3)
(c) State and use the conservative strategy to choose the best decision. (3)
(d) State and use the opportunity loss strategy to make the best decision. (3)
(e) Suppose the decision maker obtains information that enables the following probabilities assessments: P(s_1) = 0.5; P(s_2) = 0.2; P(s_3) = 0.2; and P(s_4) = 0.1. Use the expected value approach to determine the optimal strategy.
Project Capital needed Net 1 2 3 4 5 Return 1. Expand plant in Alberton 30 60 81 60 30 240 2. Build new plant in Port Elizabeth 60 30 120 60 60 300 3. Enlarge small machine capacity in Rosslyn 30 15 60 30 0 120 4. Enlarge large machine capacity in Rosslyn 90 60 30 30 30 210
Explanation / Answer
B1.
Solution:
Decision variables
Let P1 = { 1 if the plant in Alberton should be expanded
0 if not.
P2, P3 and P4 are similar for the other three projects.
Let Ai = amount invested in year i (i = 1, 2, 3, 4, 5.)
The model
MAX RETURN = 240 P1 + 300 P2 + 120 P3 + 210 P4
subject to
(Year 1) 30 P1 + 60 P2 + 30 P3 + 90 P4 + A1 = 150
(Year 2) 60 P1 + 30 P2 + 15 P3 + 60 P4 + A2 = 135 + 1,12 A1
(Year 3) 81 P1 + 120 P2 + 60 P3 + 30 P4 + A3 = 210 + 1,12 A2
(Year 4) 60 P1 + 60 P2 + 30 P3 + 30 P4 + A4 = 120 + 1,12 A3
(Year 5) 30 P1 + 60 P2 + 30 P4 + A5 = 90 + 1,12 A4
and
P1, P2, P3, P4 are zero-one variables
A1, A2, A3, A4, A5 0.
Optimal solution
The optimal solution is to:
• expand the plant in Alberton
• enlarge the small machine capacity in Rosslyn
• enlarge the large machine capacity in Rosslyn
• invest an amount of R39 000 in year 3, R43 680 in year 4 and R78 922 in year 5
• the net return on the chosen projects is R570 000.
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