The Dynamic Manufacturing Company is planning the expansion of one of its production departments to cope with surging market demand. T are given he three products will be manufactured in the new department and their relevant annual demand, operating times per unit, setup times and batch sizes are given below. The company operates on the basis of $2,000$ operating hours per year and plans to provide a capacity cushion of $10\%$ Product Annual Demand Operating Time$/$unit Setup Time per Batch Batch Size X$115,0000\mathrm{.}1$ Hour$4$ Hours $5,000$ Units X$28,0000\mathrm{.}2$ Hour$2$ Hours$2,000$ Units X$317,0000\mathrm{.}15$ Hour $3$ Hours $1,700$ Units The number of machines that will be required to produce the annual demand is