Q1) Jeweller and her apprentice make silver pins and necklaces by hand. Every week they have 80 hours of labour and 36 ounces of silver available.  It needs 8 hours of labour and 2 ounces of silver to make a pin, and 10 hours of labour and 6 ounces of silver to make a necklace. Every pin also comprises a small gem of some kind. Demand for pins is no more than six per week. Pin earns jeweller $400 in profit, and necklace earns $100. Jeweller desires to know how many of each item to make each week to maximize profit.

i) Create the integer programming model for this problem (written in format similar to way Problems 1 and 2 were presented).

ii) Solve this problem using computer (note: if using QM for Windows, make sure to use Integer and Mixed Integer Programming Module).