The Bloom & Blossom Company wants to expand its activities. In the next few year
ID: 3329327 • Letter: T
Question
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:
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 line a r integer programming model. Do not solve the model !
Year Amount 1 R150 000 2 R135 000 3 R210 000 4 R120 000 5 R90 000Explanation / Answer
Lets say x1,x2,x3 and x4 are decision variables for project-1,project-2,project-3 and project-4 respectively.
x1,x2,x3 and x4 can be either 0 or 1 (if 0 then respective project is not chosen and if 1 then respective project is chosen).
Objective Function: Maximize Z= 240*x1 + 300*x2 + 120*x3 +210*x4
Subject to:
30*x1 + 60*x2 + 30*x3 + 90*x4 <= 150
60*x1 + 30*x2 + 15*x3 + 60*x4 <= 135
81*x1 + 120*x2 + 60*x3 + 30*x4 <= 210
60*x1 + 60*x2 + 30*x3 + 30*x4 <= 120
30*x1 + 60*x2 + 0*x3 + 30*x4 <= 90
xi = 0 or 1 for i=1,2,3,4
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