Question 2 Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $63, $95, and $135, respectively. The production requirements per unit are as follows: Answer the following questions (a-i) using the output below 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 and what is the value of the objective function b) Which constraints are binding and which constraint show extra capacity? c) 100 hours of manufacturing time became available. Evaluate the effect? Explain
Question 2
Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $63, $95, and $135, respectively. The production requirements per unit are as follows:
Answer the following questions (a-i) using the output below 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 and what is the value of the objective function
b) Which constraints are binding and which constraint show extra capacity?
c) 100 hours of manufacturing time became available. Evaluate the effect? Explain
d) The profit per unit for deluxe model was increased to 150 per unit. Evaluate the effect
e) . Identify the range of optimality for each objective function coefficient (unit profit). Suppose the profit for the economy model is increased by $6 per unit, the profit for the standard model is decreased by $2 per unit, and the profit for the deluxe model is increased by $4 per unit. (use the 100% rule)What will be the new optimal solution be?
f) If the number of fan motors available for production is increased by 100, evaluate the effect.
g) What are the allowable values within the number of cooling coils can vary without affecting the shadow price?
h) Is the problem degenerate? Explain!
i) Are there alternative optima in this problem? Explain
j) What value should be in the slack column that is given by ????
![Microsoft Excel 12.0 Answer Report
Worksheet: [Assignment 1 S1 2012-13 solutions.xls]Q 2 LP sensitivity (2)
Report Created: 9/16/2012 1:05:22 PM
Microsoft Excel 12.0 Sensitivity Report
Worksheet: [Assignment 1 S1 2012-13 solutions.xls]Q 2 LP sensitivity (2)
Report Created: 9/16/2012 1:05:22 PM
Target Cell (Max)
Adjustable Cells
Original
Value
Reduce
Allowabl
Allowabl
Cell
Name
Final Value
Objective
Coefficien
Final
d
$E$4 profit
16440
Valu
Cell
Name
Cost
Increase
Decrease
number of units
Adjustable Cells
$B$3 Economy
80
63
12
15.5
$C$3 number of units standard
120
95
31
8
Original
Value
$D$
3
Cell
Name
Final Value
number of units
number of units deluxe
-24
135
24
1E+30
$B$3 Economy
80
$C$3 number of units standard
120
Constraints
$D$3 number of units deluxe
Constrain
Allowabl
Allowabl
Final
Shadow
Valu
Cell
Name
Price
R.H. Side
Increase
Decrease
Constraints
$E$6 Fan motors
200
31
200
80
40
Cell
Name
Cell Value
Formula
Status
Slack
$E$7 cooling coils
320
32
320
80
120
$E$6 Fan motors
200 $E$6<=$G$6 Binding
320 $E$7<=$G$7 Binding
$E$8 Manuf time
2080
2400
1E+30
320
$E$7 cooling coils
Not
$E$8 Manuf time
2080 $E$8<=$G$8 Binding
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