A company which makes chocolate bars needs to buy some exotic nuts: walnuts, chestnuts, and hazelnuts. They do not have to buy any of any one type, but they do need to satisfy certain combinations of types, which has been modelled using three constraints. Also, there is a capacity restriction. The model has been formulated as:

Let X1, X2, and X3 represent respectively the number of kilograms of walnuts, chestnuts, and hazelnuts to be used each hour in the chocolate bar plant.

minimize2X1 + 7X2 + 4X3

subject to

Combination 15X1 + 8X2 + 6X3 230

Combination 22X1 + X2 + 4X3 145

Combination 33X1 + 4X2 + 5X3 196

Capacity8X1 + 9X2 + 4X3 252

non-negativity X1 , X2 , X3 0

(a)Solve using a spreadsheet Solver, and create the Answer and Sensitivity Reports. (2 marks)

(b)State the solution in words, and indicate which constraints are binding.(1 mark)

(c)By using the information from the Sensitivity Report (NOT by re-running the model each time), give the predicted change to the objective function value (and the reasoning behind your answer) for the following situations (where each situation is independent of the others). If the OFV cannot be predicted exactly, then give an answer such as "the OFV will decrease by at least $50".

(i) An extra 100 units of capacity becomes available.(1 mark)

(ii) The requirement for combination 1 falls by 25 units.(1 mark)

(iii) The requirement for combination 3 increases by 92 u