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

- 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.

- 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?

- For what values of the price of a type 2 radio would the current basis remain optimal?
- If laborer 1 is willing to work only 30 hours per week, would the current basis remain optimal?
- If laborer 2 is willing to work up to 60 hours per week, would the current basis remain optimal?
- If laborer 1 were willing to work an additional hour, what is the most Radioco should be willing to pay?
- 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.
- 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?

- Letting
be the number of type
- In solving the linear program
subject to

we obtain the optimal tableau

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

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

Tue Jul 21 13:15:11 SST 1998