Mr Lee has $1650$ gemstone beads and $1950$ crystal beads. He wants to use all the beads to make nec

Question

Mr Lee has $1650$ gemstone beads and $1950$ crystal beads. He wants to use all the beads to make necklaces of three different designs: Classic, Elegant and Deluxe. The number of gemstone and crystal beads required to make one necklace of each design are as shown. If Mr Lee must make at least one necklace of each design, find the maximum and minimum number of Deluxe necklaces that he can make. [3] If the total number of Classic and Elegant necklaces that Mr Lee makes is the same as the number of Deluxe necklaces, determine the number of necklaces of each design that he makes. [2] Mr Lee decides not to make any Deluxe necklaces and makes only Classic and Elegant necklaces. State, with a reason, whether he is able to do so if all the beads must be used. [1]

Accepted Answer

(i) Minimum 71; maximum 114 Deluxe necklaces. (ii) 10 Classic, 70 Elegant, 80 Deluxe. (iii) Impossible: it would require $x=-70$.

2019 HCI C1BT1 Q3

2019 HCI C1BT1 Q3

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