5 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 per week, 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, would the current basis remain optimal? Find the new optimal solution to the LP.
e Find the shadow price of each constraint.

Transcribed Image Text:

max z = 3x1 + 2x2 s.t. x1 + 2x2 40 2x1 + x2 50 x1, x20