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 $6 per hour. The price as well as the resources required to build each type of radio are given in Table 1. Letting x; be the number of Type i radios produced each week, Radioco should solve the following LP: max z = 3x + 2x s.t. x + 2x = 40 2x + x 50 X1, X 0 For what values of the price of a Type 1 radio would the current basis remain optimal? b For what values of the price of a Type 2 radio would the current basis remain optimal? TABLE 1 Price ($) 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.