Zephyr Ltd: learning curve and cost forecasting

Tick each point that your answer made clearly and only once. Points here are this site's own. A real examiner may accept other valid points.

• The cumulative average time for 8 batches = 200 x 8^-0.2345 = 200 x 0.85^3 = 122.82 hours.
• Total time for 8 batches = 8 x 122.82 = 982.6 hours.
• Labour cost for 8 batches = 982.6 x $12 = $11,791.
• The cumulative average time for 4 batches = 200 x 0.85^2 = 144.50 hours, so the total for 4 batches is 578.0 hours.
• Hours for batches 5 to 8 = 982.6 - 578.0 = 404.6 hours.
• Cost of batches 5 to 8 = 404.6 x $12 = $4,855.
• The steady state: if the learning effect stops after a certain batch, time per batch is constant after that and the calculation is adjusted.
• The learning curve applies when work is repetitive and the workforce is stable.

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Tick each point that your answer made clearly and only once. Points here are this site's own. A real examiner may accept other valid points.

• n = 6, sum of x = 99, sum of y = 567, sum of xy = 9898, sum of x squared = 1769.
• b = (n x sum xy - sum x x sum y) / (n x sum x2 - (sum x) squared) = 4.0037, which is $4.00k per thousand units (variable cost).
• a = (sum y - b x sum x) / n = 28.44, which is $28,439 a month (fixed cost).
• The forecast for output of 30 (thousand) is 28.44 + 4.0037 x 30 = 148.5, which is $148,550.
• The correlation coefficient r = 0.998, which shows a very strong positive linear relationship.
• The coefficient of determination r squared = 0.997, so about 99.7% of the variation in cost is explained by output.
• The method uses all the data points, and not just two like the high-low method.
• The calculations are laid out with a table of x, y, xy and x squared.

Marks counted: 0 of 8

Tick each point that your answer made clearly and only once. Points here are this site's own. A real examiner may accept other valid points.

• The forecast of 30,000 units is outside the range of the data (10,000 to 24,000), so it is an extrapolation, and the relationship may not hold, for example if fixed costs step up.
• The correlation is very strong, which gives some confidence, but there are only six data points.
• The learning curve assumes a stable workforce and repetitive work, and the learning effect may stop (steady state).
• Both techniques depend on past data, which may not reflect future conditions, such as price rises or process changes.
• Data quality and the cost of collecting it affect reliability.

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