Fixed and Variable Costs

A production analyst evaluates different levels of automation for quality control inspection of whole-kernel cut corn. 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-colored kernels. Option 2 involves using fewer employees who only check for off-colored 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 work station, and small bursts of air. This new machine can automatically inspect individual kernels of corn for size and color as the conveyor 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 the analyst expected the initial costs of the options vary substantially. He investigated the cost of each option and has summarized the information in the following table:

Option 1 Option 2 Option 3
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Annual fixed Cost $ 2,500 $ 4,500 $ 27,000

Variable cost per $100 $80 $20
thousand pounds

Requirements (ensure you graph functions)

1. Based on annual cost, determine the annual volume (in thousand 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 annul cost of each option if annual volume (in thousand pounds) is 50, 200, 350, and 500. Circle the lowest cost at each annual volume.
3. Based 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?