# PBA4804 Decision Support Systems For Managers

## Question:

The Delux Nut Company produces a deluxe mix composed of almonds, cashews, peanuts and walnuts.The deluxe mix must contain at least 10% of each kind of nut. At least half of the mix must be composed of almonds and cashews and it can contain at most 20% peanuts. The company also produces a companion mix composed of cashews, walnuts and raisins. This mix must contain at least 10% cashews, at least 30% walnuts, and between 20% and 40% raisins. Raisins are available in unlimited supply at a purchasing cost of R3,60 per kilogram. The quantities of nuts available and the purchasing costs in rand per kilogram are as follows:

Both mixes are sold in 100 g packages. The company must produce at least 4 000 packages of the deluxe mix and at least 5 000 packages of the companion mix.
(a) Formulate an LP model for this problem.
(b) Solved the LP using LINGO or SOLVER
(c) Write down the optimal purchasing plan and the associated purchasing costs.
(d) The suppliers inform the company that the availability of almonds has been reduced to 200 kg and that of peanuts to 100 kg. How will this influence the optimal plan and purchasing costs Give reasons for your answer.
(e) An extra 50 kg of walnuts can be bought at R11,00 per kg. Would you make use of this offer Give reasons for your answer.

(f) Assume that the optimal plan is obtained from the original available quantities of nuts. The company now decides that it must produce at least 4 500 packages of the deluxe mix. Will the total purchasing costs be influenced? Give reasons for your answer.
(e) The supplier of peanuts announces a 40% increase in price. What will the effect of this be? Give reasons for your answer.

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.
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, 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!

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