Fashion Designs produces four clothing products – pants, dresses, skirts and blouses. The company needs to make at least 300 garments in total. Further, the number of blouses produced should be more than the number of skirts by at least 20. The firm has 800 hours of cutting time, 720 hours of sewing time and 600 hours of packing and inspecting time. Each pant requires 1 hour of cutting time, 4 hours of sewing time and 2 hours of packing and inspecting time. Each dress requires 1 hour of cutting time, 2 hours of sewing time and 2 hours of packing and inspecting time. Each skirt requires 4 hours of cutting time, 1 hour of sewing time and 1 hour of packing and inspecting time. Each blouse requires 1 hour of cutting time, 3 hours of sewing time and 1 hour of packing and inspecting time. The profit from a pant, dress, skirt and blouse are respectively $15, $16, $12 and $16. Decision Variables P - # of pants to produce D - # of dresses to produce S - # of skirts to produce B - # of blouses to produce Objective function Maximize z = 15P + 16D + 12S + 16B Constraints Cutting: P + D + 4S + B < 800 Sewing: 4P + 2D + S + 3B < 720 Packing & Inspect: 2P + 2D + S + B < 600 Min. production: P + D + S + B > 300 Blouse & skirt: B > S + 20 P,D,S,B > 0 The sensitivity report for the problem is given below. Each statement in the following questions refers to the original problem. In other words, each statement is independent of other statements. For each statement given you are asked to determine if the optimal solution changes or not. Suppose that profit per pant increases to $25.How will this impact the optimal point and the value of the objective function value?
Fashion Designs produces four clothing products – pants, dresses, skirts and blouses. The company needs to make at least 300 garments in total. Further, the number of blouses produced should be more than the number of skirts by at least 20. The firm has 800 hours of cutting time, 720 hours of sewing time and 600 hours of packing and inspecting time. Each pant requires 1 hour of cutting time, 4 hours of sewing time and 2 hours of packing and inspecting time. Each dress requires 1 hour of cutting time, 2 hours of sewing time and 2 hours of packing and inspecting time. Each skirt requires 4 hours of cutting time, 1 hour of sewing time and 1 hour of packing and inspecting time. Each blouse requires 1 hour of cutting time, 3 hours of sewing time and 1 hour of packing and inspecting time. The profit from a pant, dress, skirt and blouse are respectively $15, $16, $12 and $16.
Decision Variables
P - # of pants to produce
D - # of dresses to produce
S - # of skirts to produce
B - # of blouses to produce
Objective function
Maximize z = 15P + 16D + 12S + 16B
Constraints
Cutting: P + D + 4S + B < 800
Sewing: 4P + 2D + S + 3B < 720
Packing & Inspect: 2P + 2D + S + B < 600
Min. production: P + D + S + B > 300
Blouse & skirt: B > S + 20
P,D,S,B > 0
The sensitivity report for the problem is given below.
Each statement in the following questions refers to the original problem. In other words, each statement is independent of other statements. For each statement given you are asked to determine if the optimal solution changes or not.
Suppose that profit per pant increases to $25.How will this impact the optimal point and the value of the objective function value?
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