The Alpine Sports Company makes a line of winter sports equipment, including skis, snowboards, and sleds. Each product uses time on an extruder machine and requires time in final assembly. In addition, each product is largely made of fiberglass. They have formulated a linear programming spreadsheet model to determine the production levels that would maximize profit. The spreadsheet model and sensitivity report are shown below. Answer the following questions as completely as is possible without re-solving the problem with Solver. Justify your answers using the results from the sensitivity report. All problems are independent (i.e., any change made in one part does not affect the other parts). A F G H 1 Alpine Sports 2 Skis (pair) $90 3 Snowboard Sled 4 Profit Per Unit $140 $110 5 Available 7200 Resources Resources Required per Unit Produced Totals Extruder (minutes) Final Assembly (minutes) Fiberglass (pounds) 7 8 4 7200 8 10 12 8 12780 14400 3D> 9 4 12 15 9000 <= 9000 10 11 Skis (pair) Snowboard Sled Total Profit 12 Production 630 540 $132,300 Variable Cells Reduced Allowable Objective Coefficient Final Allowable Cll Name Value Cost Increase Decrease $C$12 $D$12 $E$12 Production Skis (pair) Production Snowboard Production Sled 630 90 190 43.33 540 140 130 45 -58.5 110 58.5 1E+30 Constraints Shadow Constraint Allowable Allowable Final Value Cell Name Price R.H. Side Increase Decrease $F$7 Extruder (minutes) Totals Final Assembly (minutes) Totals 12780 Fiberglass (pounds) Totals 7200 6.5 7200 1800 4200 $F$8 $F$9 14400 9000 1E+30 2314.29 1620 5400 9000 9.5 d. Suppose they discover that 1000 pounds of fiberglass is defective and therefore unusable. How much would this affect total profit? Will this cause a change in the optimal production quantities? e. Suppose the extruder breaks down temporarily, thus reducing the time available in extruding by 5 hours and they obtain 200 more pounds of fiberglass. How much will this affect total profit? Will this cause a change in the optimal production quantities?
The Alpine Sports Company makes a line of winter sports equipment, including skis, snowboards, and sleds. Each product uses time on an extruder machine and requires time in final assembly. In addition, each product is largely made of fiberglass. They have formulated a linear programming spreadsheet model to determine the production levels that would maximize profit. The spreadsheet model and sensitivity report are shown below. Answer the following questions as completely as is possible without re-solving the problem with Solver. Justify your answers using the results from the sensitivity report. All problems are independent (i.e., any change made in one part does not affect the other parts). A F G H 1 Alpine Sports 2 Skis (pair) $90 3 Snowboard Sled 4 Profit Per Unit $140 $110 5 Available 7200 Resources Resources Required per Unit Produced Totals Extruder (minutes) Final Assembly (minutes) Fiberglass (pounds) 7 8 4 7200 8 10 12 8 12780 14400 3D> 9 4 12 15 9000 <= 9000 10 11 Skis (pair) Snowboard Sled Total Profit 12 Production 630 540 $132,300 Variable Cells Reduced Allowable Objective Coefficient Final Allowable Cll Name Value Cost Increase Decrease $C$12 $D$12 $E$12 Production Skis (pair) Production Snowboard Production Sled 630 90 190 43.33 540 140 130 45 -58.5 110 58.5 1E+30 Constraints Shadow Constraint Allowable Allowable Final Value Cell Name Price R.H. Side Increase Decrease $F$7 Extruder (minutes) Totals Final Assembly (minutes) Totals 12780 Fiberglass (pounds) Totals 7200 6.5 7200 1800 4200 $F$8 $F$9 14400 9000 1E+30 2314.29 1620 5400 9000 9.5 d. Suppose they discover that 1000 pounds of fiberglass is defective and therefore unusable. How much would this affect total profit? Will this cause a change in the optimal production quantities? e. Suppose the extruder breaks down temporarily, thus reducing the time available in extruding by 5 hours and they obtain 200 more pounds of fiberglass. How much will this affect total profit? Will this cause a change in the optimal production quantities?
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Transcribed Image Text:Alpine Sports
The Alpine Sports Company makes a line of winter sports equipment, including skis, snowboards, and sleds. Each
product uses time on an extruder machine and requires time in final assembly. In addition, each product is largely
made of fiberglass. They have formulated a linear programming spreadsheet model to determine the production
levels that would maximize profit. The spreadsheet model and sensitivity report are shown below. Answer the
following questions as completely as is possible without re-solving the problem with Solver. Justify your answers
using the results from the sensitivity report. All problems are independent (i.e., any change made in one part
does not affect the other parts).
A
В
C
F
G
1 Alpine Sports
2
Skis (pair)
$90
Snowboard
$140
3
Sled
4
Profit Per Unit
$110
Resources
Resources Required per Unit Produced
Totals
Available
Extruder (minutes)
Final Assembly (minutes)
Fiberglass (pounds)
7
8
4
4
7200
<=
7200
10
12
8
12780
<=
14400
9.
4
12
15
9000
<ニ
9000
10
11
Skis (pair)
Snowboard
Sled
Total Profit
12
Production
630
540
$132,300
Variable Cells
Final
Reduced
Allowable
Allowable
Objective
Coefficient
Cell
Name
Value
Cost
Increase
Decrease
$C$12
$D$12
$E$12
Production Skis (pair)
630
90
190
43.33
Production Snowboard
540
140
130
45
Production Sled
-58.5
110
58.5
1E+30
Constraints
Shadow
Price
Final
Constraint
Allowable
Allowable
Cell
Name
Value
R.H. Side
Increase
Decrease
$F$7
Extruder (minutes) Totals
Final Assembly (minutes) Totals 12780
Fiberglass (pounds) Totals
7200
6.5
7200
1800
4200
$F$8
$F$9
14400
1E+30
1620
9000
9.5
9000
2314.29
5400
d. Suppose they discover that 1000 pounds of fiberglass is defective and therefore unusable. How much would
this affect total profit? Will this cause a change in the optimal production quantities?
e. Suppose the extruder breaks down temporarily, thus reducing the time available in extruding by 5 hours
and they obtain 200 more pounds of fiberglass. How much will this affect total profit? Will this cause a change
in the optimal production quantities?
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