The 3J Company manufactures handbags, shoulder bags, and backpacks. The construction of the three products requires leather and synthetics, with leather being the limiting raw material. The production process uses two types of skilled labor: sewing and finishing. The following table gives the daily availability of the resources, their usage by the three products, and the prices per unit. Leather (ft³) Sewing (hr) Finishing (hr) Price in Pesos Hand bag 3 2 2 1200 Requirement per Unit Shoulder bag Backpack 4 3 2 2250 2 1.5 1 1100 Availability 45 43 47 a. Define the decision variables and formulate a linear programming model for this problem. b. Find the optimal solution using the Excel Solver and interpret the result. c. Determine the binding constraints.

Purchasing and Supply Chain Management
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ISBN:9781285869681
Author:Robert M. Monczka, Robert B. Handfield, Larry C. Giunipero, James L. Patterson
Publisher:Robert M. Monczka, Robert B. Handfield, Larry C. Giunipero, James L. Patterson
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The 3J Company manufactures handbags, shoulder bags, and
backpacks. The construction of the three products requires leather and synthetics,
with leather being the limiting raw material. The production process uses two types of
skilled labor: sewing and finishing. The following table gives the daily availability of the
resources, their usage by the three products, and the prices per unit.
Leather (ft²)
Sewing (hr)
Finishing (hr)
Price in Pesos
Hand bag
3
2
2
1200
Requirement per Unit
Shoulder bag
2
1.5
1
1100
Backpack
4
3
2
2250
Availability
45
43
47
a. Define the decision variables and formulate a linear programming model for this
problem.
b. Find the optimal solution using the Excel Solver and interpret the result.
c. Determine the binding constraints.
d. Consider an independent case for each decision variable. Find the range of prices
for handbag, shoulder bag and backpack that makes the optimal solution remain
unchanged.
e. Determine the new optimal solution when the available leather is increased to 47 ft².
f. Determine the new optimal solution when the available finishing hours is decreased
to 15 ft².
g. Interpret the dual prices given in the sensitivity analysis report of the original problem.
h. Interpret the values under the reduced cost column found in the sensitivity analysis
report of the original problem.
Transcribed Image Text:The 3J Company manufactures handbags, shoulder bags, and backpacks. The construction of the three products requires leather and synthetics, with leather being the limiting raw material. The production process uses two types of skilled labor: sewing and finishing. The following table gives the daily availability of the resources, their usage by the three products, and the prices per unit. Leather (ft²) Sewing (hr) Finishing (hr) Price in Pesos Hand bag 3 2 2 1200 Requirement per Unit Shoulder bag 2 1.5 1 1100 Backpack 4 3 2 2250 Availability 45 43 47 a. Define the decision variables and formulate a linear programming model for this problem. b. Find the optimal solution using the Excel Solver and interpret the result. c. Determine the binding constraints. d. Consider an independent case for each decision variable. Find the range of prices for handbag, shoulder bag and backpack that makes the optimal solution remain unchanged. e. Determine the new optimal solution when the available leather is increased to 47 ft². f. Determine the new optimal solution when the available finishing hours is decreased to 15 ft². g. Interpret the dual prices given in the sensitivity analysis report of the original problem. h. Interpret the values under the reduced cost column found in the sensitivity analysis report of the original problem.
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Consider an independent case for each decision variable. Find the range of prices
for handbag, shoulder bag and backpack that makes the optimal solution remain
unchanged.
e. Determine the new optimal solution when the available leather is increased to 47 ft2
.
f. Determine the new optimal solution when the available finishing hours is decreased
to 15 ft2
.

g. Interpret the dual prices given in the sensitivity analysis report of the original problem.
h. Interpret the values under the reduced cost column found in the sensitivity analysis
report of the original problem.

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