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3. 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.
Minimize 2X1 + 7X2 + 4X3
subject to 5X1 + 8X2 + 6X3 Ã¢â€°Â¥ 230 (Combination 1)
2X1 + X2 + 4X3 Ã¢â€°Â¥ 145 (Combination 2)
3X1 + 4X2 + 5X3 Ã¢â€°Â¥ 196 (Combination 3)
8X1 + 9X2 + 4X3 Ã¢â€°Â¤ 252 (Capacity)
X1, X2, X3 Ã¢â€°Â¥ 0 (Non-negativity)
(a) Solve the model using a spreadsheet Solver, and create the Answer and Sensitivity Reports.
(b) Present the solution in words, and indicate which constraints are binding.
(c) By using the information from the Sensitivity Report (without resolving the model), 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 objective function value cannot be predicted exactly, then give an answer such as “the objective function value will decrease by at least $50”.
(i) The price of hazelnuts rises by $1.20 per kg.
(ii) The price of chestnuts falls by $2.70 per kg.
(iii) An extra 100 units of capacity becomes available.
(iv) The requirement for combination 1 falls by 25 units.
(v) The requirement for combination 3 increases by 92 units.
(vi) The price of walnuts rises by 15 cents per kg, while the price of hazelnuts falls by 40 cents per kg.
(vii) The price of chestnuts falls by $4 per kg, while the price of hazelnuts rises by $1 per kg.
(viii)The right-hand side value of Combination 3 rises by 80 units, while the RHS of Capacity rises by 20 units.
(ix) The RHS of Combination 3 decreases by 4 units, while the RHS of Capacity constraint increases by 21 units. 4. A power company has a maximum
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