yasaswi gomes 24 November 2020
| n=9 | Forecasted sales demand (X) | Actual sales demand | Total Fixed costs | Total Variable costs | Total unit Price (Y) | XY | X² | Y² |
| 2010 | 100 | 110 | 100 | 50 | 1.36 | 136.36 | 10000 | 1.86 |
| 2011 | 120 | 115 | 100 | 50 | 1.30 | 156.52 | 14400 | 1.70 |
| 2012 | 90 | 100 | 100 | 50 | 1.50 | 135.00 | 8100 | 2.25 |
| 2013 | 110 | 130 | 100 | 50 | 1.15 | 126.92 | 12100 | 1.33 |
| 2014 | 140 | 150 | 100 | 50 | 1.00 | 140.00 | 19600 | 1.00 |
| 2015 | 120 | 120 | 100 | 50 | 1.25 | 150.00 | 14400 | 1.56 |
| 2016 | 120 | 100 | 100 | 50 | 1.50 | 180.00 | 14400 | 2.25 |
| 2017 | 150 | 170 | 100 | 50 | 0.88 | 132.35 | 22500 | 0.78 |
| 2018 | 140 | 150 | 100 | 50 | 1.00 | 140.00 | 19600 | 1.00 |
| 2019 | 130 | 150 | 100 | 50 | 1.00 | 130.00 | 16900 | 1.00 |
| Total | 1220 | 1295 | 1000 | 500 | 11.95418 | 1427.161 | 152000 |
14.73323504 |
| Workings: | ||||||||||||
| X= | Σ X/n= | 1295/9= | 143.8889 | |||||||||
| Y= | Σ Y/n= | 11.95418/9= | 1.328243 | |||||||||
| Least Squares Method | ||||||||||||
| Constant b= | Σ XY - n(X)(Y)= | -292.913 | = | 0.008531 | ||||||||
| (Σ X²)-n(X)² | -34336.1 | |||||||||||
| Constant a= | Y-bX= | 30919.32- (311.2415 * 135.5556) | ||||||||||
| = | 0.100763 | |||||||||||
| Y= a + bX | = | 50 | Price/Unit | |||||||||
| Optimal Pricing of Products | ||||||||||||
| 0.100763 - 0.008531 (X) | = | 50 | ||||||||||
| 0.008531 (X) | = | 50+(0.100763) | ||||||||||
| X (Demand in units) | = | 5873 | ||||||||||
| Y (Price/Unit) | = | 50 | ||||||||||
| Units to be produced | = | 5873 | ||||||||||
| Price per unit | = | 50 | ||||||||||
| Profits are maximised when Marginal Revenue= Marginal Cost (Variable Cost) | ||||||||||||
| Total Revenue= | 294832 | |||||||||||
| Total Costs= Fixed cost+ (X*Variable cost) | 294648 | |||||||||||
| Profit | 184 | |||||||||||
| Extrapolated results for Linear Equations: | ||||||||||||
| Y= a + bX | This Demand Curve linear equation directly calculates the optimal selling price when Units to be produced are given to maximise revenues | |||||||||||
| Y= a - bX | This Demand Curve linear equation maximises profits when the equation is simplified for MR=MC | |||||||||||
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