Question

2. A vendor sells three different packages of mixed nuts. The budget mix contains 300g of peanuts, 50 g of Brazil nuts and 150g of cashew nuts. The special mix contains 200g of peanuts, 200g of Brazil nuts and 100g of cashews, while the exotic mix contains 100g of peanuts, 350g of Brazil nuts and 50g of cashew nuts. On a specific day, he has in stock 30 kg of peanuts, 15 kg of Brazil nuts and 15 kg of cashews. 1 marks (a) Set up a system of equations to represent the information above. (b) Represent the system found in (a) by an augmented matrix, and transform this into reduced 3 marks] row echelon form (c) The vendor knows that his profit on the budget mix is $0.50 per bag, whereas on the special mix he makes a profit of $1.50 per bag and on the exotic mix he makes $2 profit per bag. How many bags of each type of mix should the vendor make if he wants to use up all of 3 marks the nuts and maximise his profit?

Answer 1

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