The linear programming equations are expressing information

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Reference no: EM132285921

Linear Programming

Chemicals, Inc. is a petroleum manufacturing plant located in the Middle East. It has been in existence over the past 15 years. They are currently working on their strategic plans for the year 2019 to 2025. The growth of export petroleum sales over the past couple of years has been good, but the sales could grow even more if the planned high-tech oil refinery is built near the city where Chemicals, Inc. is located. Chemicals, Inc, is considering three strategies. First is to increase its current production operations, the second is to move closer to the proposed new oil refinery, and the third is to do nothing. Strong growth as a result of the presence of the new oil refinery has a 55 percent probability and moving closer to it, would give annual returns of $390,000 per year. Weak growth, however, would mean annual returns of $230,000. If nothing was done in the first year of 2015, and strong growth occurred, the strategy to increase its current production would be reconsidered. Strong growth with an increased production would give annual returns of $380,000 per year. Weak growth, however, would mean annual returns of $200,000. With no changes, there would be returns of $340,000 per year if there is strong growth and $210,000 per year if growth is weak. Increasing production will cost $ 174,000 and moving to a location closer to the refinery will cost $ 420,000. If growth is strong and the production is increased during the second year, the cost would also be $174,000. The cost to operate is the same for all strategies. After reviewing their options based on the decision trees and recommendations, Chemicals, Inc. realized that doing nothing will generate more profits and benefits than the other two alternatives. However, they wanted to develop an improved aviation fuel to be used by commercial jets at minimal cost. The fuel is a mixture of two fuels (Avgas A and Avgas B). There are 4,000 gallons of Avgas A and 8,000 gallons of Avgas B available. It needs no fewer than 6,000 gallons to fuel a jet to its farthest destination which has a maximum fuel storage capacity of 8,000 gallons. The mixed fuel must have an octane rating of no less than 80. The octane rating is the weighted average of the individual octanes, weighted in proportion to the respective volumes. During mixture, the amount of Avgas obtained equals to the sum of the amounts put in. Avgas A has an octane of 95 and costs $2.40 per gallon. Avgas B has an octane of 75 and costs $1.80 per gallon. In presenting your findings to Chemicals, Inc., they would like to see:

a. The linear programming equations are expressing this information. (Show Your Work Step by Step)

b. Your solutions using the graphical method. (Show Your Work Step by Step)

c. The optimal point that will satisfy the objective function (Show Your Work Step by Step)

d. The final optimal equation that would meet their objective. (Show Your Work Step by Step)

Reference no: EM132285921

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