Questions: Middle Industries produces a sensor for use in manufacturing. It produces the sensor in a plant with an annual practical capacity of 75,000 units. The variable cost of the sensor is 185.00 per unit, and the fixed costs of the plant are 12,375,000 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 75,000 sensors? What would be the cost of excess capacity?

To address the questions, we need to calculate the cost per sensor and the cost of excess capacity based on the given data. Let's break down each part of the question:

1. Variable Cost per Sensor: \[ \text{Variable Cost per Sensor} = \$185.00 \]

2. Fixed Costs: \[ \text{Fixed Costs} = \$12,375,000 \text{ annually} \]

3. Current Annual Demand: \[ \text{Current Annual Demand} = 55,000 \text{ sensors} \]

4. Total Cost: \[ \text{Total Cost} = \text{Variable Cost} + \text{Fixed Costs} \]

5. Total Variable Cost: \[ \text{Total Variable Cost} = 55,000 \text{ sensors} \times \$185.00/\text{sensor} = \$10,175,000 \]

6. Total Cost: \[ \text{Total Cost} = \$10,175,000 + \$12,375,000 = \$22,550,000 \]

7. Cost per Sensor: \[ \text{Cost per Sensor} = \frac{\text{Total Cost}}{\text{Current Annual Demand}} = \frac{\$22,550,000}{55,000 \text{ sensors}} = \$410.00/\text{sensor} \]

1. Practical Capacity: \[ \text{Practical Capacity} = 75,000 \text{ sensors} \]

2. Excess Capacity: \[ \text{Excess Capacity} = \text{Practical Capacity} - \text{Current Annual Demand} = 75,000 \text{ sensors} - 55,000 \text{ sensors} = 20,000 \text{ sensors} \]

3. Fixed Cost per Sensor: \[ \text{Fixed Cost per Sensor} = \frac{\text{Fixed Costs}}{\text{Practical Capacity}} = \frac{\$12,375,000}{75,000 \text{ sensors}} = \$165.00/\text{sensor} \]

4. Cost of Excess Capacity: \[ \text{Cost of Excess Capacity} = \text{Excess Capacity} \times \text{Fixed Cost per Sensor} = 20,000 \text{ sensors} \times \$165.00/\text{sensor} = \$3,300,000 \]

1. Total Cost: \[ \text{Total Cost} = \text{Variable Cost} + \text{Fixed Costs} \]

2. Total Variable Cost: \[ \text{Total Variable Cost} = 75,000 \text{ sensors} \times \$185.00/\text{sensor} = \$13,875,000 \]

3. Total Cost: \[ \text{Total Cost} = \$13,875,000 + \$12,375,000 = \$26,250,000 \]

4. Cost per Sensor: \[ \text{Cost per Sensor} = \frac{\text{Total Cost}}{75,000 \text{ sensors}} = \frac{\$26,250,000}{75,000 \text{ sensors}} = \$350.00/\text{sensor} \]

5. Cost of Excess Capacity: \[ \text{Cost of Excess Capacity} = 0 \text{ (since the plant is fully utilized)} \]

• Part (a): The cost per sensor for management decision making is \$410.00.
• Part (b): The cost of excess capacity is \$3,300,000.
• Part (c): If the smallest manufacturing plant could produce 75,000 sensors, the cost per sensor would be \$350.00, and the cost of excess capacity would be \$0.