Environmental Planning
You are the operations manager of a chemical company which produces five products in a
common production facility. The following table gives potential sales for each product, along
with variables costs and revenues. Production in any year cannot exceed the sales potential.
Information needed – Attached files.
Your production facility rotates through the product line because it can produce only one product
at a time. The production rates differ for the various products. It takes 0.3 hours to make 1 ton of
A, 0.5 hour for a ton of B, and 1 hour each for a ton of C, D, or E. The facility can be operated
up to 4000 hours per year.
The file EnviroPlanning.xlsx contains all the information given above in a format designed for
optimization. Use this template to answer the following questions. – FIle Attached
a. Determine the maximum profit the company can achieve from its product line in the coming
year.
$____________________
b. What is the shadow price on the sales potential for product C?
$____________________
Parts (c), (d) and (e) are independent: changes described in one part do not apply to the other
parts. For example, part (c) involves changing the sales potential of product C from 1000 to 2500
tons. For parts (d) and (e), the sales potential should be set back to the original 1500 tons.
c. Describe in words how the optimal production plan and profit change as the sales potential on
Product C changes from 1000 to 2500 tons.
d. An engineering firm is offering to improve the efficiency of the process for manufacturing
products C, D, and E. This process improvement will reduce the time required for all three
products by up to 10%. How big an improvement to all three products is necessary in order to
offset the cost of $30,000? Your answer should be a percentage between 0% and 10% (answer to
the nearest integer percentage). Include a table of results to justify your answer.
Required improvement: ___________
TABLE:
e. The EPA is proposing to limit particulate emissions from your company over the next five
years to the amounts specified below. The sales potential for each of the five products is
expected to remain stable over this period.
Year Total Emissions
(tons)
Y:1 TE:100
Y:2 TE:80
Y:3 TE:60
Y:4 T:E40
Y:5 TE:20
The emissions produced by each product are given below.
Product Particulate Emissions
(tons/ton produced)
A 0.0010
B 0.0025
C 0.0300
D 0.0400
E 0.0250
The company plans to satisfy these requirements by modifying the product mix each year. What
would the optimal profits be in each of the next five years?
Year Profit
1 $______________
2 $______________
3 $______________
4 $______________
5 $______________
