Solutions Operations management

Solution) Costal States produces eight (8) chemical products that are sold to companies in various industries.

Question: Costal States produces eight (8) chemical products that are sold to companies in various industries. Information about the products that Costal States provides on a daily basis is shown in the table below. This table shows profit margin for each product, capacity at each plant for producing the product and the consumption of natural gas required to produce each product. Additionally, the table shows the maximum production rate percentage that can be ascertained for each product on a daily basis. This maximum production rate for each product takes into account market demand requirements for each product and potential system losses in the production process. Note, that Costal States produces only one product (Ammonium Nitrate) to it’s maximum production rate, no other product is be produced at its full capacity rate.

An important ingredient to the production process is natural gas as this provides the heating for the furnaces in the production of each chemical product. The amount of natural gas required for each product is also detailed in the table

PRODUCT	*Profit* *(Dollars per Ton)*	*Capacity* *(Tons Per Day)*	*Maximum Production Rate* *(% of Capacity)*	*Natural Gas Consumption* *(1,000 cubic feet per ton)*
PHOSPHORIC ACID	$60	400	80	5.5
UREA	$80	250	80	7.0
AMMONIUM PHOSPHATE	$90	300	90	8.0
AMMONIUM NITRATE	$100	300	100	10.0
CHLORINE	$50	800	60	15.0
CAUSTIC SODA	$50	1,000	60	16.0
VINYL CHLORIDE MONOMER	$65	500	60	12.0
HYDROFLUORIC ACID	$70	400	80	11.0

Costal States receives 36,000 cubic feet of natural gas per day from Cajun Pipelines. Recently, Cajun Pipelines has informed Costal States that it may see a reduction in natural gas supply by either 20% or 40% in the pursuing winter months. This curtailment is the result of government energy regulations. Use Linear Programming (not integer) to determine the following:

a. What is Costal States maximum profit with no curtailment in the natural gas resource

b. What is the impact to maximum profit and chemical production with a 20% curtailment of natural gas resource

c. What is the impact to maximum profit and chemical production with a 40% curtailment of natural gas resource

d. Suppose there is a 40% curtailment in natural gas resource. How much would Costal be willing to pay for additional gas resources (Assume Costal States is only looking to break even (no additional profits) and how much resources would they purchase at this price (answer this from the confines of sensitivity analysis for the model)

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