SOLVE IN EXCEL SOLVER

2.9. Production Planning with Environmental Constraints You are the Operations Manager of Lovejoy Chemicals, Inc., which produces five products in a common production facility that will be subject to proposed Environmental Protection Agency (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 as follows (note: T denotes tons).

Your 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 due to 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 is proposing a bubble policy for your industry. In this form of regulation, imagine that a bubble encloses the manufacturing facility, and only total particulates that escape the bubble are regulated. This sort of policy replaces historical attempts by the EPA to micromanage emissions within a firm, and it allows Lovejoy to make any changes it wishes, provided the total particulate emissions from its facility are kept below certain limits. The current proposal is to phase-in strict particulate emissions limits over the next five years. These limits on total particulate emissions are shown in the table below.

One strategy for satisfying these regulations is to adjust the product mix, cutting back on production of some products if necessary. Lovejoy wishes to explore this strategy before contemplating the addition of new equipment.

(a) Determine the maximum profit Lovejoy can achieve from its product line in the coming year (Year 1).

(b) By solving a series of models corresponding to the imposition and tightening of the emissions limit in future years, determine Lovejoys maximum profits in each of Years 25.

(c) Consider the emissions limit that applies in Year 4. Determine how much Lovejoy should be willing to pay at that time to be allowed emissions of one extra ton of particulates above the limit.

Sales Variable potential costs ($/T Revenues ($/T) Particulate emissions /T produced) Product (T/year) 2000 1600 1000 1000 600 700 600 1000 1600 1300 1000 800 1500 2000 1700 0.0010 0.0025 0.0300 0.0400 0.0250 Year 1 unlimited 2 80 3 60 4 40 5 20 Allowable emissions (T/year) Sales Variable potential costs ($/T Revenues ($/T) Particulate emissions /T produced) Product (T/year) 2000 1600 1000 1000 600 700 600 1000 1600 1300 1000 800 1500 2000 1700 0.0010 0.0025 0.0300 0.0400 0.0250 Year 1 unlimited 2 80 3 60 4 40 5 20 Allowable emissions (T/year)