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:

Nut

Purchasing costs in rand

Kilogram available

Almonds

Cashews

Peanuts

Walnuts

12,00

10,60

2,80

8,40

400

200

600

300

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.