Modeling is an art, and it takes practice. The following examples show the variety of problems that can be attacked by linear programming, and give you the opportunity to try your hand at some problems.

Answers to Exercise 61:

(a) *Let be the number of toasters produced manually, be
the number produced semiautomatically, and be the number
produced robotically.
*

*
The objective is to Minimize .
*

*
The constraints are:
*

*
(produce enough toasters)
*

*
(skilled labor used less than or equal to
amount available).
*

*
(unskilled labor constraint)
*

*
(assembly time constraint)
*

*
(nonnegativity of production)
*

*
*

(b)
*Add a constraint *

(c)
*Add a variable to represent the assembly time slack. Add
to the objective. Change the assembly time constraint to
*

*
(assembly time constraint)
*

*
*

Mon Aug 24 16:30:59 EDT 1998