Calculation of Reliability and Total Cost

The U.S. Army is about to award a contract for an electrical switching device to Integrated Switches Corporation (ICS) of Phoenix, Arizona. The switch will be used on the next version of infantry carrier vehicles. One obstacle that remains to be resolved,
However, is that the Army requires a reliability of 0.995 for the device. ICS is studying its test data to determine if there is a practical way that its product can be made to meet the Army's reliability requirement. The switching device has four critical interacting component parts with the following test data:

Number
Component Number of of Hours Number
Part Parts Tested of Testing of Failures
B13 400 2,500 2
X9 650 3,800 1
M22 275 1,750 0
R5 1,600 4,200 3

Delana Lightfoot is a production analyst at the Golden Kernel processing plant, which processes whole-kernel cut corn. Delana's current project is to evaluate different levels of automation for quality control inspection of corn kernels. Option 1 is to assign a number of employees along the conveyor belt to inspect the corn kernels manually as they go by and pick out small and off-color kernels. Option 2 involves using fewer employees who only check for off-color kernels and then running the corn over a screen that filters out the small kernels, Option 3 is to purchase a state-of-the-art, fully automated machine that uses video cameras, a computer workstation, and small bursts of air. The new machine can automatically inspect individual kernels of corn for size and color as the conveyer belt moves the kernels in a single layer by the machine. Inferior kernels are removed by a precisely placed small burst of air as the kernels pass over a perforated air tube.

As Delana expected, the initial costs of the options vary substantially. She investigated the cost of each option and has summarized the information in the following table:

Option 1 Option 2 Option 3
Annual fixed cost 2,500 $4,500 $27,000
Variable cost per 100 80 20
Thousand pounds

Questions:

1. Based on annual cost, determine the annual volume (in thousands of pounds) at which the company would be indifferent between Option 1 and Option 2; between Option 2 and Option 3; and between Option 1 and Option 3.
2. Create a table showing the total annual cost of each option if annual volume (in thousands of pounds) is 50,200,350, and 500. Circle the lowest cost at each annual volume.
3. Based only on annual cost, for what range of annual volumes would each option be preferred?
4. What factors other than annual cost should be considered when making this decision?