Maximize: Z P C D

Where: P total discounted profit over life of new products

C change in either direction in current level of employment

D decrease if any in next years earnings from current years level

The amount of any increase in earnings does no enter into Z because management is concerned primarily with just achieving some increase to keep the stockholders happy. It has mixed feelings about a large increase that then would be difficult to surpass in subsequent years.

The impact of each of the new products per unit rate of production on each of these factors is shown in the following table:

Factors Unit Contribution Goals Units

Product

Longrun profit Maximize millions of dollars

Employment level hundreds of employees

Earnings next year millions of dollars

a Assuming that there are no additional constraints on the production rates not described here, use the goal programming technique to formulate a linear programming model for this problem.