22 Radioco manufactures two types of radios. 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 Table 61.

a Letting xi be the number of type i radios produced each week, show that Radioco should solve the following LP (its optimal tableau is given in Table 62):

b For what values of the price of a Type 1 radio would the current basis remain optimal?
c For what values of the price of a Type 2 radio would the current basis remain optimal?
d If laborer 1 were willing to work only 30 hours per week, would the current basis remain optimal?
e If laborer 2 were willing to work as many as 60 hours per week, would the current basis remain optimal?
f If laborer 1 were willing to work an additional hour, what is the most that Radioco should pay?
g If laborer 2 were willing to work only 48 hours, what would Radioco’s profits be? Verify your answer by determining the number of radios of each type that would be produced.
h A Type 3 radio is under consideration for production.
The specifications of a Type 3 radio are as follows:
price, $30; 2 hours from laborer 1; 2 hours from laborer 2; cost of raw materials, $3. Should Radioco manufacture any Type 3 radios?

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TABLE 61 Price ($) Radio 1 25 Resource Required Price ($) Laborer 1: 22 1 hour Laborer 2: 2 hours Raw material cost: $5 TABLE 62 Z Radio 2 Resource Required Laborer 1: 2 hours Laborer 2: 2 hours Raw material cost: $4 rhs 1 0 0 0 1 0 0 0 1 -mm lm 4 80 2 3 WOWN W 3 2 20 1 10