1

The Bloom & Blossom Company wants to expand its activities.In the next fewyearsa 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

R90000

Four projects are being considered.The capital needed per year for each project (in R1000) and the present value of the net return (in R1000) on each project are given in the table below.

Capital needed

Net

Project

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

If a project is selected, ithas tobe completed as a whole.Capitalnot 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.

(a)Define the decision variables that will be needed to formulate a linear programming (LP) model for this problem(5 marks)

(b)Formulate the problem aslinear integer programmingmodel.(15 marks)

(c)Solve this model with SOLVER.(15 marks)

(d)Interpret your SOLVER solution within the context of the original business problem.(5marks)