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. Dining Assembly (minutes) Finishing (minutes) Wood (pounds) Unit Profit Rocking Chair 100 60 30 $240 Room Table 180 80 180 $720 Armoire 120 80 120 $600 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. Available 3.600 2,000 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. 4,000 d) Because of sickness of I worker in the assembly dept, 4 hours of assembly was lost, evaluate the effect. h) Is the problem degenerate? Explain! i) Are there alternative optima in this problem? Explain i) What value should be in the slack column that is given by ???? 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?
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. Dining Assembly (minutes) Finishing (minutes) Wood (pounds) Unit Profit Rocking Chair 100 60 30 $240 Room Table 180 80 180 $720 Armoire 120 80 120 $600 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. Available 3.600 2,000 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. 4,000 d) Because of sickness of I worker in the assembly dept, 4 hours of assembly was lost, evaluate the effect. h) Is the problem degenerate? Explain! i) Are there alternative optima in this problem? Explain i) What value should be in the slack column that is given by ???? 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?
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter3: Introduction To Optimization Modeling
Section3.8: A Multiperiod Production Model
Problem 18P: The Pigskin Company produces footballs. Pigskin must decide how many footballs to produce each...
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Transcribed Image Text: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.
Dining
Assembly
(minutes)
Finishing
(minutes)
Wood
(pounds)
Unit Profit
Rocking
Chair
100
60
30
$240
Room Table
180
80
180
$720
Armoire
120
80
120
$600
Available
3,600
2,000
4,000
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.
h) Is the problem degenerate? Explain!
i) Are there alternative optima in this problem? Explain
i) What value should be in the slack column that is given by ????
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?
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