Radioco manufactures two types of radios. The only scarce resource needed to produce radios is…

Radioco manufactures two types of radios. The only scarce resource needed to produce radios is labor. The company now has two laborers. Laborer 1 is willing to work as many as 40 hours per week and is paid \$5 per hour. Laborer 2 is willing to work up to 50 hours per week and is paid \$6 per hour. The price as well as the resources required to build each type of radio are given in Table 1.
Letting xi be the number of type i radios produced each week, show that Radioco should solve the following LP: a. For what values of the price of a Type 1 radio would the current basis
Radioco manufactures two types of radios. The only scarce resource needed to produce radios is labor. The company now has two laborers. Laborer 1 is willing to work as many as 40 hours per week and is paid \$5 per hour. Laborer 2 is willing to work up to 50 hours per week and is paid \$6 per hour. The price as well as the resources required to build each type of radio are given in Table 1.
Letting xi be the number of type i radios produced each week, show that Radioco should solve the following LP: a. 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?
c. If laborer 1 were willing to work only 30 hours perweek, 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 perweek, would the current basis remain optimal? Find the new optimal solution to the LP.
e. Find the shadow price of each constraint.

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