Radioco manufactures two types of radios. The only scarce resource that is needed to produce radios...
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Radioco manufactures two types of radios. The only scarce resource that is needed to produce radios is labor. At present, the company has two laborers. Laborer 1 is willing to work up to 40 hours per week and is paid $5 per hour. Laborer 2 will work up to 50 hours per week for $6 per hour. The price as well as the resources required to build each type of radio are given in Table 1. Letting x; be the number of Type i radios produced each week, Radioco should solve the following LP: max z = 3x₁ + 2x₂ s.t. x₁ + 2x₂ = 40 2x₁ + x₂ 50 X1, X₂ ≥ 0 For what values of the price of a Type 1 radio would the current basis remain optimal? b For what values of the price of a Type 2 radio would the current basis remain optimal? TABLE 1 Price ($) 25 Radio 1 Resource Required Laborer 1: 1 hour Laborer 2: 2 hours Raw material cost: $5 Price ($) 22 Radio 2 Resource Required Laborer 1: 2 hours Laborer 2: 2 hours Raw material cost: $4 C c If laborer 1 were willing to work only 30 hours per week, then would the current basis remain optimal? Find the new optimal solution to the LP. d If laborer 2 were willing to work up to 60 hours per week, then would the current basis remain optimal? Find the new optimal solution to the LP. Radioco manufactures two types of radios. The only scarce resource that is needed to produce radios is labor. At present, the company has two laborers. Laborer 1 is willing to work up to 40 hours per week and is paid $5 per hour. Laborer 2 will work up to 50 hours per week for $6 per hour. The price as well as the resources required to build each type of radio are given in Table 1. Letting x; be the number of Type i radios produced each week, Radioco should solve the following LP: max z = 3x₁ + 2x₂ s.t. x₁ + 2x₂ = 40 2x₁ + x₂ 50 X1, X₂ ≥ 0 For what values of the price of a Type 1 radio would the current basis remain optimal? b For what values of the price of a Type 2 radio would the current basis remain optimal? TABLE 1 Price ($) 25 Radio 1 Resource Required Laborer 1: 1 hour Laborer 2: 2 hours Raw material cost: $5 Price ($) 22 Radio 2 Resource Required Laborer 1: 2 hours Laborer 2: 2 hours Raw material cost: $4 C c If laborer 1 were willing to work only 30 hours per week, then would the current basis remain optimal? Find the new optimal solution to the LP. d If laborer 2 were willing to work up to 60 hours per week, then would the current basis remain optimal? Find the new optimal solution to the LP.
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Answer rating: 100% (QA)
a Current basis x1 20 x2 10 Objective value z 3x1 2x2 320 210 60 Constraints x1 2x2 40 2x1 x2 50 Che... View the full answer
Related Book For
Practical Management Science
ISBN: 9781305250901
5th edition
Authors: Wayne L. Winston, Christian Albright
Posted Date:
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