Uncle Ulysses operates a small business: he produces three types of houses to sell to people...

 

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Uncle Ulysses operates a small business: he produces three types of houses to sell to people wanting to get back to nature. Based on your discussion with your uncle you construct the following table based on your understanding of his weekly availability of labor. Item Profit/Unit Fabrication Assembly Painting Crating Birdhouse $15 1 2.5 1 0.25 Doghouse $35 1.25 1.5 0.5 0.5 $58 1.75 4 2 0.75 Outhouse Capacity 30 hours 50 hours 20 hours 20 hours Based on the information in the table, you formulate the problem as a linear program. The labor needed for fabrication, assembly, painting, and crating is all dedicated solely to each function, i.e., none of the workers have been cross-trained. You solved the problem using Excel and generated the following sensitivity report. Variable Cells Final Cell Name Value $C$4 Birdhouse 0.00 $D$4 Doghouse 15.38 $E$4 Outhouse 6.15 Constraints Cell Name $F$5 Fabricate $F$6 Assemble $F$7 Paint $F$8 Crate Final Value 30.00 47.69 20.00 12.31 Reduced Cost -17.15 0.00 0.00 Shadow Price 25.23 0.00 6.92 0.00 Objective Allowable Allowable Coefficient Increase Decrease 17.15 1E+30 6.43 20.50 82.00 9.00 15.00 35.00 58.00 Constraint Allowable R.H. Side Increase 30 3.75 50 1E+30 20 1.58 20 1E+30 Allowable Decrease 12.50 2.31 8.00 7.69 After some market investigation, Uncle Ulysses decided to increase the price of Doghouse from $35 to $40. Will this change the current optimal production plan? If we refer to the four constraints as "Fabricate", "Assemble", "Paint" and "Crate". Which constraints are NOT binding? In a week, due to workers' vacation plan, Uncle Ulysses only has 15 painting hours. How would his profit of this week be affected and why? Uncle Ulysses operates a small business: he produces three types of houses to sell to people wanting to get back to nature. Based on your discussion with your uncle you construct the following table based on your understanding of his weekly availability of labor. Item Profit/Unit Fabrication Assembly Painting Crating Birdhouse $15 1 2.5 1 0.25 Doghouse $35 1.25 1.5 0.5 0.5 $58 1.75 4 2 0.75 Outhouse Capacity 30 hours 50 hours 20 hours 20 hours Based on the information in the table, you formulate the problem as a linear program. The labor needed for fabrication, assembly, painting, and crating is all dedicated solely to each function, i.e., none of the workers have been cross-trained. You solved the problem using Excel and generated the following sensitivity report. Variable Cells Final Cell Name Value $C$4 Birdhouse 0.00 $D$4 Doghouse 15.38 $E$4 Outhouse 6.15 Constraints Cell Name $F$5 Fabricate $F$6 Assemble $F$7 Paint $F$8 Crate Final Value 30.00 47.69 20.00 12.31 Reduced Cost -17.15 0.00 0.00 Shadow Price 25.23 0.00 6.92 0.00 Objective Allowable Allowable Coefficient Increase Decrease 17.15 1E+30 6.43 20.50 82.00 9.00 15.00 35.00 58.00 Constraint Allowable R.H. Side Increase 30 3.75 50 1E+30 20 1.58 20 1E+30 Allowable Decrease 12.50 2.31 8.00 7.69 After some market investigation, Uncle Ulysses decided to increase the price of Doghouse from $35 to $40. Will this change the current optimal production plan? If we refer to the four constraints as "Fabricate", "Assemble", "Paint" and "Crate". Which constraints are NOT binding? In a week, due to workers' vacation plan, Uncle Ulysses only has 15 painting hours. How would his profit of this week be affected and why?

Answer rating: 100% (QA)

To determine whether the change in the price of the Doghouse will affect the current optimal production plan we need to examine the sensitivity report ... View the full answer