Lecture-Notes-Part-3-Regression-LP-1.pdf

They have advised him that they can only sell about

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They have advised him that they can only sell about 3,000 S1’s, 800 S2’s and 1,500 S3’s next year. Joe has provided the following information: Year Production Labour Hours S1 S2 S3 Total 1 897 466 776 2,139 24,392 2 1,296 512 828 2,636 29,953 3 1,365 550 913 2,828 31,974 4 1,377 582 978 2,937 33,129 5 1,682 622 1,037 3,341 37,516 6 1,793 648 1,055 3,496 39,378 7 1,907 633 1,091 3,631 40,318 8 2,233 670 1,189 4,092 45,062 9 2,369 735 1,307 4,411 48,544 10 2,503 776 1,493 4,772 51,985 Wood costs $25 per metre. Labour costs $40/hour. Unfortunately, Joe doesn’t know how many hours are used to build each type of snowboard, just the totals for each year of production. Joe leases a shop for $500,000 per year for SSI’s snowboard production. 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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Prepared by J. Kroeker, 2017 © Sauder School of Business, UBC jkaccounting.ca 126 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 Square 0.999312295 Coefficients Standard Error Intercept 2378.087284 341.0715916 Total 10.45620649 0.096979438 b) Provide an estimate for fixed labour hours. c) What is Joe’s objective function to maximize profit? d) Using the regression you chose, estimate Joe’s profit for the current year (i.e. year #10 in the table above): e) If labour was 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. Regression #2 R Square 0.999968894 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 Square 0.982553633 Coefficients Standard Error Intercept 22647 827.9641503 Year 2832.381818 133.4385051
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Prepared by J. Kroeker, 2017 © Sauder School of Business, UBC jkaccounting.ca 127 f) If wood was constrained to current year usage levels (i.e. year 10), with no labour constraint. What would Joe’s optimal production plan be within the demand constraints of his supplier? Assume no fixed labour . g) Joe decides that he must be realistic about next year’s production and that he should take all the constraints into account. What are his constraints for next year? (mathematical formulas) h) What is Joe’s optimal production plan for next year, and what is his profit?
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Prepared by J. Kroeker, 2017 © Sauder School of Business, UBC jkaccounting.ca 128 Swarthy Snow Industries: How confident are you in the model? Final Objective Allowable Allowable Name Value Coefficient Increase Decrease Production S1 3,000.00 191.60 Infinity 54.13 Production S2 699.10 314.80 123.95 314.80 Production S3 1,500.00 108.50 Infinity 36.46 Final Shadow Constraint Allowable Allowable Name Value Price R.H. Side Increase Decrease S1 Demand 3,000.00 54.13 3,000.00 312.26 231.05 S2 Demand 699.10 K 800.00 Infinity 100.90 S3 Demand 1,500.00 36.46 1,500.00 337.51 440.93 Labour (hours) used 55,000.00 13.46 55,000.00 2,359.00 16,345.00 Wood (meters) used 9,648.20 K 10,000.00 Infinity 351.80 Using the information provided in the question and the table above, explain how confident you are on this being the optimal model (provide calculations and rationale). Regression #2 R Squared 0.99 Coefficients Standard Error Intercept 254.30 311.31 S1 10.20 0.16 S2 23.37 1.311 S3 5.34 0.47
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Prepared by J. Kroeker, 2017 © Sauder School of Business, UBC jkaccounting.ca 129 LP, relevant costs & decision-making Nieve Ltd. produces three products for the snowboard industry. The three products are all bindings: Basic, Advanced and Extreme. The selling prices are: Basic $ 39.50 Advanced $ 65.00 Extreme $170.00 The production process uses plastic as its main material and this costs $4 per kilogram, labor is $20 per hour and variable machining costs are $30 per hour on machine 1 and $50 per hour on machine 2.
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