A B C D E F. 1 Year Real Home Price Index 2 1946 106.5 3 1947 109.3 4 4 1948 101.2 5 1949 100.0 6 1950 105.9 7 1951 103.9 8 1952 104.0 9 1953 114.7 10 1954 114.2 11 1955 115.5 12 1956 115.3 13 14 15 16 17 18 19 20 A B C D E F. G 1 Problem Description 2 A production manager wants to determine how many units of each product to produce weekly to maximize weekly profits. Production requirements for the products are show in the following table: 3 4 5 Product Material 1 (lbs) Material 2 (lbs) Labor (hours) Profit/unit 6 A 3 2 4 10 7 B 1 4 2 10 8 C 5 0 3.5 10 9 10 11 Each week there are 300 pounds of material 1; 400 pounds of material 2; and 200 hours of labor. There is a standing order of 10 units of product Ceach week. The LP model formulation of this problem is shown below 12 13 14 LP FORMULATION 15 Ma xi mize 10A + 10B + 10C PROFIT 16 Subject to: 17 3A + B + 5C =10 MIN UNITS OF PRODUCT C 21 A,B,C >= 0 NON-NEGATIVITY CONSTRAINT B D E F G y 10 11 Each week there are 300 pounds of material 1:400 pounds of material 2; and 200 hours of labor. There is a standing order of 10 units of product Ceach week. The LP model formulation of this problem is shown below 12 13 14 15 PROFIT MATERIAL 1 AVAILABLE 16 17 18 19 LP FORMULATION Maximize 10A + 10B - 100 Subject to: 3A + B + 5C C=300 24 + 4B 10 ABC > 0 MATERIAL 2 AVAILABLE LABOR HOURS AVAILABLE 20 MIN UNITS OF PRODUCT C 21 NON-NEGATIVITY CONSTRAINT 22 23 SENSITIVITY REPORT Adjustable cells 24 25 Final Value Reduced Cost Objective Coefficient Cell Name 26 27 - 10 10 $B$4 $C$4 $ $D$4 28 Allowable Allowable Increase Decrease 10 15-30 15-30 4.285 7.5 15-30 Units produced: A Units produced: Units produced: C 82.5 0 10 29 10 0 10 Constraints 30 31 32 33 Shadow Final Value Constraint R.H.S. Side Allowable Increase Allowable Decrease Cell Name Price 34 D 300 15-30 167.5 132.5 330 35 0 400 1E-30 $E$7 $ SE$8 SE$9 SE$10 Material 1 Available Material 2 Available Labor hrs Available Min Units of 70 165 36 200 5 200 35 37 10 -7.5 10 47.142 10 Q1-Q5 Shiller Home Q9-Q14 Production Q26-27 Brown Q28-029 Mortgage Payoff A B D E F. 1 2 Outcome 3 0.6 0.3 0.1 Probability Decision 4 Rates Rise Rates Stable Rates Fall 5 1-year ARM $ 66,645.00 43,650.00 $ 38,560.00 6 3-year ARM $ 62,857.00 $ 47,698.00 $ 42,726.00 7 5-year ARM $ 55,895.00 $ 50,894.00 $ 48,134.00 8 30-year fixed $ 52,276.00 $ 52,276.00 $ 52,276.00 9 10 11 12 13 14 15 16 17 18 19 20 Question Setting k=4, determine the value of mean absolute percent error of years 1950 - 1956. 3.88% B 4.15% 3.34% (D) 3.55% Question 3 For which value of k is the forecast most accurate based on the MAE for years 1950-1956? A k=2 k=3 k=4 A B C D E F. 1 Year Real Home Price Index 2 1946 106.5 3 1947 109.3 4 4 1948 101.2 5 1949 100.0 6 1950 105.9 7 1951 103.9 8 1952 104.0 9 1953 114.7 10 1954 114.2 11 1955 115.5 12 1956 115.3 13 14 15 16 17 18 19 20 A B C D E F. G 1 Problem Description 2 A production manager wants to determine how many units of each product to produce weekly to maximize weekly profits. Production requirements for the products are show in the following table: 3 4 5 Product Material 1 (lbs) Material 2 (lbs) Labor (hours) Profit/unit 6 A 3 2 4 10 7 B 1 4 2 10 8 C 5 0 3.5 10 9 10 11 Each week there are 300 pounds of material 1; 400 pounds of material 2; and 200 hours of labor. There is a standing order of 10 units of product Ceach week. The LP model formulation of this problem is shown below 12 13 14 LP FORMULATION 15 Ma xi mize 10A + 10B + 10C PROFIT 16 Subject to: 17 3A + B + 5C =10 MIN UNITS OF PRODUCT C 21 A,B,C >= 0 NON-NEGATIVITY CONSTRAINT B D E F G y 10 11 Each week there are 300 pounds of material 1:400 pounds of material 2; and 200 hours of labor. There is a standing order of 10 units of product Ceach week. The LP model formulation of this problem is shown below 12 13 14 15 PROFIT MATERIAL 1 AVAILABLE 16 17 18 19 LP FORMULATION Maximize 10A + 10B - 100 Subject to: 3A + B + 5C C=300 24 + 4B 10 ABC > 0 MATERIAL 2 AVAILABLE LABOR HOURS AVAILABLE 20 MIN UNITS OF PRODUCT C 21 NON-NEGATIVITY CONSTRAINT 22 23 SENSITIVITY REPORT Adjustable cells 24 25 Final Value Reduced Cost Objective Coefficient Cell Name 26 27 - 10 10 $B$4 $C$4 $ $D$4 28 Allowable Allowable Increase Decrease 10 15-30 15-30 4.285 7.5 15-30 Units produced: A Units produced: Units produced: C 82.5 0 10 29 10 0 10 Constraints 30 31 32 33 Shadow Final Value Constraint R.H.S. Side Allowable Increase Allowable Decrease Cell Name Price 34 D 300 15-30 167.5 132.5 330 35 0 400 1E-30 $E$7 $ SE$8 SE$9 SE$10 Material 1 Available Material 2 Available Labor hrs Available Min Units of 70 165 36 200 5 200 35 37 10 -7.5 10 47.142 10 Q1-Q5 Shiller Home Q9-Q14 Production Q26-27 Brown Q28-029 Mortgage Payoff A B D E F. 1 2 Outcome 3 0.6 0.3 0.1 Probability Decision 4 Rates Rise Rates Stable Rates Fall 5 1-year ARM $ 66,645.00 43,650.00 $ 38,560.00 6 3-year ARM $ 62,857.00 $ 47,698.00 $ 42,726.00 7 5-year ARM $ 55,895.00 $ 50,894.00 $ 48,134.00 8 30-year fixed $ 52,276.00 $ 52,276.00 $ 52,276.00 9 10 11 12 13 14 15 16 17 18 19 20 Question Setting k=4, determine the value of mean absolute percent error of years 1950 - 1956. 3.88% B 4.15% 3.34% (D) 3.55% Question 3 For which value of k is the forecast most accurate based on the MAE for years 1950-1956? A k=2 k=3 k=4