Prepared by wdorfmann 2012 commerce 354 sauder school

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Prepared by W.Dorfmann, 2012 © Commerce 354 Sauder School of Business, UBC S1 S2 S3 Price $700 $1,500 $400 Wood 2 metres 2 metres 1.5 metres Other Materials $50 $200 $40 Max demand 3,000 800 1,500
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Swarthy Snow Industries Required: a) Which of the following regressions would you use to determine the number of labour hours required for each type of snowboard? Regression #1 R Square0.999312295 Coefficients Standard Error Intercept 2378.087284 341.0715916 Total 10.45620649 0.096979438 Regression #2 R Square0.999968894 Coefficients Standard Error Intercept 254.3024005 311.315286 S1 10.2088404 0.169892427 S2 23.3777251 1.311527816 S3 5.348076251 0.470867465 Regression #3 R Square0.982553633 Coefficients Standard Error Intercept 22647 827.9641503 Year 2832.381818 133.4385051  Regression #2 is the only one which includes all products as independent variables.  The case indicates that different boards use  different amounts of labour, so there is likely to be a multiple correlation which can be discerned by using all of the products as  independent variables against total labour hours. b) Provide an estimate for fixed labour hours.  254 hours (based on intercept), but since std err is so large in comparison, probably  better to view this as ~0 hours. c) What is Joe’s objective function to maximize profit? Maximize Total Contribution Margin = $191.60xS1+ $314.80xS2+$108.50xS3 d) Using the regression you chose, estimate Joe’s profit for the current year (i.e. year #10 in the table above): Unit contribution margin for each type of snowboard: S1 S2 S3 Price $700.00  $1,500.00  $400.00  DM ($100.00) ($250.00) ($77.50) DL ($408.40) ($935.20) ($214.00) CM $191.60  $314.80  $108.50  Profit = #2,503x$191.60 + #776x$314.80 + #1,493x$108.50 – $500,000 FC= $385,850  If you estimated fixed labour of #254 hours, the profit is reduced:  $135,850 - #254x$40 = $375,690 Prepared by W.Dorfmann, 2012 © Commerce 354 Sauder School of Business, UBC
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Swarthy Snow Industries e) If labourwas constrained to current-year usage levels (i.e. year 10), with no constraint on wood, what would Joe’s optimal production plan be within the demand constraints of his supplier? Assume no fixed labour. S1 S2 S3 CM/DLH $18.77 $13.46 $20.28 Labour constraint can be obtained from the data provided: #51985 hours.
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  • Constraint, S6, Constraint satisfaction

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