CS3252 Management Science
Tutorial # 6, September 14 - September 19, 1998

1. Radioco manufactures two types of radios. The only scarce resource needed to produce radios is labor. At present, the company has only 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 is given below.
   

   

   1. Letting be the number of type i radios produced each week, show that Radioco should solve the following linear program:

      

      subject to

      

      The optimal tableau of this linear program is as follows.

      

      For what values of the price of a type 1 radio would the current basis remain optimal?

   2. For what values of the price of a type 2 radio would the current basis remain optimal?
   3. If laborer 1 is willing to work only 30 hours per week, would the current basis remain optimal?
   4. If laborer 2 is willing to work up to 60 hours per week, would the current basis remain optimal?
   5. If laborer 1 were willing to work an additional hour, what is the most Radioco should be willing to pay?
   6. If laborer 2 were willing to work only 48 hours, what would Radioco's profit be? Verify your answer by determining the number of radios of each type that would be produced if laborer 2 were willing to work only 48 hours.
   7. 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 radio?
2. In solving the linear program

   

   subject to

   

   we obtain the optimal tableau

   

   ( and are slacks for constraint 1 and 2, respectively)

   1. Find the optimal solution to this linear program if we add the constraint
   2. Find the optimal solution to this linear program if we add the constraint (Drawing the feasible region would be helpful).
   3. Find the optimal solution to this linear program if we add the constraint