4-28. The Classic Furniture Company is trying to determine the optimal quantities to make of six possible products: tables and chairs made of oak, cherry, and pine. The products are to be made using the following resources: labor hours and three types of wood. Minimum production requirements are as follows: at least 3 each of oak and cherry tables, at least 10 each of oak and cherry chairs, and at least 5 pine chairs. The Excel layout and LP Sensitivity Report for Classic Furniture's problem are shown in Figure 4.32 and 4.33, respectively. The objective function coeffici- ents in the figures refer to unit profit per item. Each of the following questions is independent of the others. (a) What is the profit represented by the objective function, and what is the production plan? (b) Which constraints are binding? (c) What is the range over which the unit profit for oak chairs can change without changing the production plan? What is the range over which the amount of available oak could vary without changing the combination of binding constraints? Does this Sensitivity Report indicate the presence of multiple optima? How do you know? (f) After production is over, how many pounds of cherry wood will be left over? (g) According to this report, how many more chairs were made than were required? 1 Classic Furniture Company N- w $10,000.00 Oak Oak Cherry Cherry Pine Pine tables chairs tables chairs tables chairs 4 Number of units 3.00 51.67 3.00 85.56 42 26 33.08 5 Profit $75 $35 $90 $60 $45 $20 6 Constraints 7 Labor hours | 7.5 35 9.0 6.0 4.5 20 8 Oak (pounds) 200 30 9 Cherry (pounds) 240 36 10 Pine (pounds) 180 27 11 Min oak tables 12 Min cherry tables 13 Min oak chairs 14 Min cherry chairs 15 Min pine chairs 16 1000.00 1,000 2150,00 2.150 3800.00 = 3.800 8500.00 8.500 3.00 > 3.00 > 51.67 > 85.56 > 33.08 > IHS Sion RHS 4-28. The Classic Furniture Company is trying to determine the optimal quantities to make of six possible products: tables and chairs made of oak, cherry, and pine. The products are to be made using the following resources: labor hours and three types of wood. Minimum production requirements are as follows: at least 3 each of oak and cherry tables, at least 10 each of oak and cherry chairs, and at least 5 pine chairs. The Excel layout and LP Sensitivity Report for Classic Furniture's problem are shown in Figure 4.32 and 4.33, respectively. The objective function coeffici- ents in the figures refer to unit profit per item. Each of the following questions is independent of the others. (a) What is the profit represented by the objective function, and what is the production plan? (b) Which constraints are binding? (c) What is the range over which the unit profit for oak chairs can change without changing the production plan? What is the range over which the amount of available oak could vary without changing the combination of binding constraints? Does this Sensitivity Report indicate the presence of multiple optima? How do you know? (f) After production is over, how many pounds of cherry wood will be left over? (g) According to this report, how many more chairs were made than were required? 1 Classic Furniture Company N- w $10,000.00 Oak Oak Cherry Cherry Pine Pine tables chairs tables chairs tables chairs 4 Number of units 3.00 51.67 3.00 85.56 42 26 33.08 5 Profit $75 $35 $90 $60 $45 $20 6 Constraints 7 Labor hours | 7.5 35 9.0 6.0 4.5 20 8 Oak (pounds) 200 30 9 Cherry (pounds) 240 36 10 Pine (pounds) 180 27 11 Min oak tables 12 Min cherry tables 13 Min oak chairs 14 Min cherry chairs 15 Min pine chairs 16 1000.00 1,000 2150,00 2.150 3800.00 = 3.800 8500.00 8.500 3.00 > 3.00 > 51.67 > 85.56 > 33.08 > IHS Sion RHS 4-28. The Classic Furniture Company is trying to determine the optimal quantities to make of six possible products: tables and chairs made of oak, cherry, and pine. The products are to be made using the following resources: labor hours and three types of wood. Minimum production requirements are as follows: at least 3 each of oak and cherry tables, at least 10 each of oak and cherry chairs, and at least 5 pine chairs. The Excel layout and LP Sensitivity Report for Classic Furniture's problem are shown in Figure 4.32 and 4.33, respectively. The objective function coeffici- ents in the figures refer to unit profit per item. Each of the following questions is independent of the others. (a) What is the profit represented by the objective function, and what is the production plan? (b) Which constraints are binding? (c) What is the range over which the unit profit for oak chairs can change without changing the production plan? What is the range over which the amount of available oak could vary without changing the combination of binding constraints? Does this Sensitivity Report indicate the presence of multiple optima? How do you know? (f) After production is over, how many pounds of cherry wood will be left over? (g) According to this report, how many more chairs were made than were required? 1 Classic Furniture Company N- w $10,000.00 Oak Oak Cherry Cherry Pine Pine tables chairs tables chairs tables chairs 4 Number of units 3.00 51.67 3.00 85.56 42 26 33.08 5 Profit $75 $35 $90 $60 $45 $20 6 Constraints 7 Labor hours | 7.5 35 9.0 6.0 4.5 20 8 Oak (pounds) 200 30 9 Cherry (pounds) 240 36 10 Pine (pounds) 180 27 11 Min oak tables 12 Min cherry tables 13 Min oak chairs 14 Min cherry chairs 15 Min pine chairs 16 1000.00 1,000 2150,00 2.150 3800.00 = 3.800 8500.00 8.500 3.00 > 3.00 > 51.67 > 85.56 > 33.08 > IHS Sion RHS 4-28. The Classic Furniture Company is trying to determine the optimal quantities to make of six possible products: tables and chairs made of oak, cherry, and pine. The products are to be made using the following resources: labor hours and three types of wood. Minimum production requirements are as follows: at least 3 each of oak and cherry tables, at least 10 each of oak and cherry chairs, and at least 5 pine chairs. The Excel layout and LP Sensitivity Report for Classic Furniture's problem are shown in Figure 4.32 and 4.33, respectively. The objective function coeffici- ents in the figures refer to unit profit per item. Each of the following questions is independent of the others. (a) What is the profit represented by the objective function, and what is the production plan? (b) Which constraints are binding? (c) What is the range over which the unit profit for oak chairs can change without changing the production plan? What is the range over which the amount of available oak could vary without changing the combination of binding constraints? Does this Sensitivity Report indicate the presence of multiple optima? How do you know? (f) After production is over, how many pounds of cherry wood will be left over? (g) According to this report, how many more chairs were made than were required? 1 Classic Furniture Company N- w $10,000.00 Oak Oak Cherry Cherry Pine Pine tables chairs tables chairs tables chairs 4 Number of units 3.00 51.67 3.00 85.56 42 26 33.08 5 Profit $75 $35 $90 $60 $45 $20 6 Constraints 7 Labor hours | 7.5 35 9.0 6.0 4.5 20 8 Oak (pounds) 200 30 9 Cherry (pounds) 240 36 10 Pine (pounds) 180 27 11 Min oak tables 12 Min cherry tables 13 Min oak chairs 14 Min cherry chairs 15 Min pine chairs 16 1000.00 1,000 2150,00 2.150 3800.00 = 3.800 8500.00 8.500 3.00 > 3.00 > 51.67 > 85.56 > 33.08 > IHS Sion RHS
