Middle Industries produces a sensor for use in manufacturing. It produces the sensor in a plant with an annual practical capacity of $76,000$ units. The variable cost of the sensor is $$186$ per unit, and the fixed costs of the plant are $$12,540,000$ annually. Current annual demand is $55,000$ sensors$.$ Middle Industries bought the plant because it was close to its other manufacturing facilities and was available for sale when they were searching for a location. Required: a$.$ What cost per sensor should the cost system report to facilitate management decision making? b$.$ What is the cost of excess capacity? c$.$ What cost per sensor would the cost system report if the smallest manufacturing plant that could be built was able to produce $76,000$ sensors$?$ What would be the cost of excess capacity?