Lovejoy Chemicals, Inc., produces five products in a common production facility that will be subject to proposed EPA limits on particulate emissions. For each product, Lovejoys sales potentials (demand levels that Lovejoy can capture) are expected to remain relatively flat for at least the next five years. Relevant data for each product are given in the following table (T denotes tons).

Product A B C

D

Sales potential (T/year) 2000 1600

Variable costs Revenues

$/T $/T 700 1000 600 800

Particulate emissions (T/T produced) 0.0010 0.0025 0.0300 0.0400 0.0250

1000 1000 1500 1000 1600 2000 600 1300 1700

E The production facility rotates through the product line because it is capable of producing

only one product at a time. The production rates differ for the various products because of the processing needs. It takes 0.3 hours to make one ton of A, 0.5 hours for B, and one hour each to make a ton of C, D, or E. The facility can be operated up to 4000 hours each year.

The EPA regulates only the total particulates that are emitted, rather than micromanaging specific ones. The limits will be phased-in over the next five years. These limits on total emissions are shown in the following table.

Year 12345 Allowable unlimited 80 60 40 20 emissions

Formulate and solve a linear program that will determine the product mix that will maximize profits over the next five years.