Question $3$ Integer programming model $(20$ marks$)$ Westside Electronics sells $12,000$ capacitators per month to its customers. The capacitators can be produced at three different plants. The production capacity, fixed monthly setup cost, and unit variable production cost of a capacitator at each plant are given in worksheet Q$3$ in the workbook "Final$-4980$ Q$1-3$ templates.xIxs". The fixed cost of for a plant is incurred only if the plant is used to make any capacitators. If a plant is used at all, at least $3000$ capacitators per month must be produced at the plant. Determine how to minimize the company's monthly costs of meeting its customers' demands.