The only scarce resource that is needed to produce radios is labor. The company now has two laborers. Laborer 1 is willing to work up to 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 $6 per hour. The price as well as the resources required to build each type of radio are given in the following table: Radio 1 Price ($) Resource Required 25 Laborer 1: 1 hr Laborer 2: 2 hr Raw Material Cost: $5 Radio 2 Price ($) Resource Required 22 Laborer 1: 2 hr Laborer 2: 1 hr Raw Material Cost: $4 Part a Letting be the number of type i radios produced each week, show that Radioco should solve the following LP: max 3.21 + 2.12 s.t. 11 + 2x2 0 Part b (5 points): The optimal tableau for this LP is given below: 2 x 22 Si S2 RHS | 80 0 1 0 - 20 0 0 1 - 10 For what values of the price of a Type 1 radio would the current basis remain optimal? Part c For what values of the price of a Type 2 radio would the current basis remain optimal? Part d If laborer 1 were willing to work only 30 hours per week, would the current basis remain optimal? The only scarce resource that is needed to produce radios is labor. The company now has two laborers. Laborer 1 is willing to work up to 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 $6 per hour. The price as well as the resources required to build each type of radio are given in the following table: Radio 1 Price ($) Resource Required 25 Laborer 1: 1 hr Laborer 2: 2 hr Raw Material Cost: $5 Radio 2 Price ($) Resource Required 22 Laborer 1: 2 hr Laborer 2: 1 hr Raw Material Cost: $4 Part a Letting be the number of type i radios produced each week, show that Radioco should solve the following LP: max 3.21 + 2.12 s.t. 11 + 2x2 0 Part b (5 points): The optimal tableau for this LP is given below: 2 x 22 Si S2 RHS | 80 0 1 0 - 20 0 0 1 - 10 For what values of the price of a Type 1 radio would the current basis remain optimal? Part c For what values of the price of a Type 2 radio would the current basis remain optimal? Part d If laborer 1 were willing to work only 30 hours per week, would the current basis remain optimal