Chap 4. Case Problem: Environmental Protection Pg. 210 By Debbie St. George: Student #: 1086941 MC506 Quantitative Methods Methods for Managers - Start Date: July 1, 2003 Develop an approach to the problem that t hat will allow the company to determine how much m uch primary product to produce, given the limitations on the amounts of the raw material available. Include recommendations as to how the company should dispose of the liquid waste to satisfy the environmental protection guidelines. How many pounds of product K should be produced? How many pounds of product M should be produced? How many pounds of liquid waste should be specially treated and dumped into t he river? Include a discussion and analysis of the following in your report: Skillings alternative disposal strategys for the liquid waste: Alternative 1 Produce a secondary product, K, by adding 1/2 (1) lb. of raw material A to 1/2 (1) lb. of liquid waste. The market value of K is such that the net contribution to profits of a pound -$0.10. Alternative 2 Produce a secondary product, M, by adding 1/2 (1) lb. of raw material B to 1/2 (1) lb. of liquid waste. The market value of M is such that the net contribution to profits of a pound of M is $0.15. Alternative 3 Treat the liquid waste so that it meets pollution standards and then dump it. The cost of this special treatment is $0.25 per lb. of liquid waste. Skillings' goal is to maximize profits. The product generates a profit of $2.10 per pound. In each production cycle, only 5000 lbs. of raw material A and 7000 lbs. of raw material B can be used.
1. A cost analysis showing the profit contribution per pound for the primar y product, product K, and pro Let x1 = lbs. of primary product x2 = lbs. of of se secondary product K lbs. of secondary product M x3 = lbs. of liquid waste to treat for disposal x4 =
2. The optimal production pr oduction quantities and waste disposal plan, including the projected profit. Profits are determ ined by the amount of primary prim ary and secondary products produced and the amount of treated liquid waste. Therefore: $2.10x1 $0.15x3 - $0.25x4 max - $0.10x2 + Production process: The pounds of K and M produced and liquid waste treated must equal the amount am ount of liquid waste generated by the production of the primary product.
Or
x1
=
.5x2
+
.5x3
+
x4
x1
-
.5x2
-
.5x3
-
x4
=
0
Optimal solution: x1 = 3500 [primary product] x2 = 3000 [K] x3 = 0 [M] x4 = 2000 [treated waste]
3. A discussion of the value of additional pounds of each raw material. Raw material constraints: 5000 x1 .5x2 + [raw material A] 2x1 .5x3 + 7000 [raw material B]
4. A discussion of the sensitivity analysis of the objective function coefficients.
5. Comments on the accountant's recommendation to eliminate product K as an alternative: Does the recommendation appear reasonable? What is your reaction the recommendation? How would the optimal solution change if product K were eliminated?
of K is
uct M.
Skillings Industrial Chemicals, Inc., operates a refinery in southwestern Ohio near the Ohio The company's primary product is manufactured from a chemical process that requires the use of two raw materials - material A and material B. The production of 1 pound of the primary product requires the use of 1 pound of material A and 2 pounds of material B to produce 1 lb. of the primary product, 1 lb. of liquid waste and 1 lb. of solid waste by-products. The solid waste by-product is given to a local fert ilizer plant as payment for picking it up and disposing of it. The liquid waste material has no market value, so the refinery has been dumping it directly into the Ohio River. The company's manufacturing process is shown schematical
Government pollution guidelines established by the Environmental Protection Agency will no longer permit disposal of the liquid waste directly into the river. The refinery's research group has developed the following set of alternative uses for the liquid material. 1. Produce a secondary product K by adding 1 pound of raw 2. Produce a secondary product M by adding 1 pound of ra 3.Specially treat the liquid waste so that it m eets pollution st
These three alternative are depicted in Figure 4.16 Alternative for handling the refinery liquid waste.
The company's management knows that the secondary products will be low in quality and may not be very profitable. However, management also recognizes that the special treatment alternative will be a relatively expensive operation. The company's problem is to determine how to satisfy the
pollution regulations and still maintain the highest possible prof it. How should the liquid waste material be handled? Should skillings produce product K, produce product M, use the special treatment, or employ some combination of the three alternatives? Last month 10,000 pounds of the company's primary product were produced. The accounting department has prepared a cost report showing he breakdown of fixed and variable expenses that were incur
Cost Analysis for 10,000 Pounds of Primary Product Fixed costs Administrative expenses Refinery overhead
$12,000 4,000
Variable costs Raw material A
15,000
Raw material B
16,000
Direct labor Total
5,000 $52,000
In this cost analysis, the fixed-cost portion of the expenses is the same every month regardless of production level. Direct labor costs are expected to run $0.20 per pound for product K and $0.10 per pound for product M. The company's primary product sells for $5.70 per pound. Secondary products K and M sell for $0.85 and $0.65 per pound, respectively. The special treatment of the liquid waste A company accountant believes that product K is too expensive to manufacture and canno be sold at a price that recovers its material and labor cost. The accountant's recommendation is to eliminate product K as an alternative For the upcoming production period, 5000 pounds of raw material A and 7000 pounds of raw material B will be available.
River.
ly in Figure 4.15.
material A to every pound of liquid waste. material B to every pound of liquid waste. ndards before dumping it into the river.
ed during the month.
ill cost $0.25 per pound. t
