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Estimating Cost Functions for Manchester Foundry

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a. Manchester Foundry produced 45,000 tons of steel in March at a cost of £1,150,000. In April, the foundry produced 35,000 tons at a cost of £950,000. Using only these two data points, determine the cost function for Manchester following the instruction in my post in Materials.

b. Use Excel's "scatter plot" graphing function to plot the two points and the "trendline" option to determine the equation of interest. Does it match what you did manually? What is the interpretation of the equation and graph?

c. You obtain new data, 30,000 tons and a cost of 600,000. How do those values match the equation you came up with by hand? Put the point into your Excel spreadsheet and create the scatter plot and trendline. Describe the output.

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Solution Summary

This solution describes the steps for developing cost function for Manchester Foundary. The equation is developed by two methods. It also discusses why new data is so different from what we got from the equation developed earlier.

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Solution:
a. Manchester Foundry produced 45,000 tons of steel in March at a cost of £1,150,000. In April,  the foundry produced 35,000 tons at a cost of £950,000. Using only these two data points, determine the cost function for Manchester
following the instruction in my post in Materials.

There are two method by which, we can determine equation
Set of simultaneous equations:
Let x represents variable cost per unit
y represents fixed cost per unit
45000 tons of steel is produced at a cost of 1150000 pounds, it gives following equation
1150000=y+45000x ---------------(1)
35000 tons of steel is produced at a cost of 950000 pounds, it gives following equation
950000=y+35000x -------------------(2)
on subtracting eqn 2 from eqn 1 we ...

Solution provided by:
Lokesh Jain, MSc
Education
  • BEng (Hons) , Birla Institute of Technology and Science, India
  • MSc (Hons) , Birla Institute of Technology and Science, India
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