Question 2 Colonial Furniture produces hand-crafted colonial style furniture. Plans are now being made for the production of rocking chairs, dining room tables, and/or armoires over the next week. These products go through two stages of production (assembly and finishing). The table in the next column gives the time required for each item to go through these two stages, the amount of wood required (fine cherry wood), and the corresponding unit profits, along with the amount of each resource available next week. Assembly Rocking Chair Dining 180 Room Table Armoire Available 100 120 3,600 (minutes) Finishing 60 80 80 2,000 (minutes) Wood 30 180 120 4,000 (pounds) Unit Profit $240 $720 $600 A linear programming model has been formulated in a spreadsheet to determine the production levels that would maximize profit. The solved spreadsheet model and corresponding sensitivity report are shown below. Answer the following questions (a-i) using the output please be brief. If there are two possible answers one will suffice. Where necessary a range analysis must be shown. a) What is the optimal solution in words?❤ b) 350 pounds of wood were lost. Evaluate the effect. c) An extra 4 hour of finishing was available. Evaluate the effect d) Because of sickness of 1 worker in the assembly dept, 4 hours of assembly was lost, evaluate the effect. e) If the profit of armoire decrease by $50.00. Evaluate the effect? ………………… f) What is the situation if the company want to produce Chair? Evaluate the effect g) If the profit of table decrease by $60.00 and profit of armoire increase by 90. Evaluate the effect?……………… h) Is the problem degenerate? Explain!❤ i) Are there alternative optima in this problem? Explaine i) What value should be in the slack column that is given by ????◄ Objective Cell (Max) Cell $E$4 profit Name Original Value Final Value 0 16200 Variable Cells Cell Name Original Value Final Value Integer $B$3 number of units Rockin chair 0 0 Contin $C$3 number of units Dining table 0 10 Contin $D$3 number of units Armoire 0 15 Contin Constraints Cell Name Cell Value Formula Status Slack $E$6 Assembly (minutes LHS 3600 $E$6<=$G$6 Binding 0 $E$7 Finishing minutes LHS 2000 $E$7<=$G$7 Binding 0 $E$8 Wood (pounds LHS 3600 $E$8<=$G$8 Not Binding ??? Microsoft Excel 15.0 Sensitivity Report Worksheet: [Assignment 1 s1 2022-23 solution.xlsx]Q2 Report Created: 10/14/2022 9:25:11 PM Variable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$3 number of units Rockin chair $C$3 number of units Dining table $D$3 number of units Armoire 0 -230 240 230 1E+30 10 0 720 180 120 15 0 600 120 120 Constraints Final Shadow Cell Name Value Price Constraint R.H. Side Allowable Allowable Increase Decrease $E$6 Assembly (minutes LHS 3600 2 $E$7 Finishing minutes LHS 2000 4.5 3600 2000 400 600 400 400 $E$8 Wood (pounds LHS 3600 0 4000 1E+30 400

Question 2 Colonial Furniture produces hand-crafted colonial style furniture. Plans are now being made for the production of rocking chairs, dining room tables, and/or armoires over the next week. These products go through two stages of production (assembly and finishing). The table in the next column gives the time required for each item to go through these two stages, the amount of wood required (fine cherry wood), and the corresponding unit profits, along with the amount of each resource available next week. Assembly Rocking Chair Dining 180 Room Table Armoire Available 100 120 3,600 (minutes) Finishing 60 80 80 2,000 (minutes) Wood 30 180 120 4,000 (pounds) Unit Profit $240 $720 $600 A linear programming model has been formulated in a spreadsheet to determine the production levels that would maximize profit. The solved spreadsheet model and corresponding sensitivity report are shown below. Answer the following questions (a-i) using the output please be brief. If there are two possible answers one will suffice. Where necessary a range analysis must be shown. a) What is the optimal solution in words?❤ b) 350 pounds of wood were lost. Evaluate the effect. c) An extra 4 hour of finishing was available. Evaluate the effect d) Because of sickness of 1 worker in the assembly dept, 4 hours of assembly was lost, evaluate the effect. e) If the profit of armoire decrease by $50.00. Evaluate the effect? ………………… f) What is the situation if the company want to produce Chair? Evaluate the effect g) If the profit of table decrease by $60.00 and profit of armoire increase by 90. Evaluate the effect?……………… h) Is the problem degenerate? Explain!❤ i) Are there alternative optima in this problem? Explaine i) What value should be in the slack column that is given by ????◄ Objective Cell (Max) Cell $E$4 profit Name Original Value Final Value 0 16200 Variable Cells Cell Name Original Value Final Value Integer $B$3 number of units Rockin chair 0 0 Contin $C$3 number of units Dining table 0 10 Contin $D$3 number of units Armoire 0 15 Contin Constraints Cell Name Cell Value Formula Status Slack $E$6 Assembly (minutes LHS 3600 $E$6<=$G$6 Binding 0 $E$7 Finishing minutes LHS 2000 $E$7<=$G$7 Binding 0 $E$8 Wood (pounds LHS 3600 $E$8<=$G$8 Not Binding ??? Microsoft Excel 15.0 Sensitivity Report Worksheet: [Assignment 1 s1 2022-23 solution.xlsx]Q2 Report Created: 10/14/2022 9:25:11 PM Variable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$3 number of units Rockin chair $C$3 number of units Dining table $D$3 number of units Armoire 0 -230 240 230 1E+30 10 0 720 180 120 15 0 600 120 120 Constraints Final Shadow Cell Name Value Price Constraint R.H. Side Allowable Allowable Increase Decrease $E$6 Assembly (minutes LHS 3600 2 $E$7 Finishing minutes LHS 2000 4.5 3600 2000 400 600 400 400 $E$8 Wood (pounds LHS 3600 0 4000 1E+30 400

Marketing

20th Edition

ISBN:9780357033791

Author:Pride, William M

Publisher:Pride, William M

Chapter19: Pricing Concepts

Section: Chapter Questions

Problem 6DRQ

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