8 A sweet shop sells three different types of boxes of chocolate truffles. The cost of each type of box and the number of truffles of each variety in each type of box are given in the table below. Narendra wants to buy some boxes of truffles so that in total he has at least 20 milk chocolate, 10 plain chocolate, 16 white chocolate and 12 nutty chocolate truffles.

1. Explain why Narendra needs to buy at least four boxes of truffles.
2. Narendra decides that he will buy exactly four boxes. Determine the minimum number of Assorted boxes that Narendra must buy.
3. For your answer in part (ii),
   • list all the feasible solutions and
   • find the cheapest solution.
   Narendra finds that the sweet shop has sold out of Assorted boxes, but he then spots that it also sells small boxes of milk chocolate truffles and small boxes of nutty chocolate truffles. Each small box contains 4 truffles (all of one variety) and costs \(\pounds 0.50\). He decides to buy \(x\) boxes of No Nuts and \(y\) boxes of Speciality, where \(x + y < 4\), so that he has at least 10 plain chocolate and 16 white chocolate truffles. He will then buy as many small boxes as he needs to give a total of at least 20 milk chocolate and 12 nutty chocolate truffles.
4. (a) Set up constraints on the values of \(x\) and \(y\).
   (b) Represent the feasible region graphically.
   (c) Hence determine the cheapest cost for Narendra. {www.ocr.org.uk}) after the live examination series. If OCR has unwittingly failed to correctly acknowledge or clear any third-party content in this assessment material, OCR will be happy to correct its mistake at the earliest possible opportunity. For queries or further information please contact the Copyright Team, First Floor, 9 Hills Road, Cambridge CB2 1GE.
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