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ID: 3283322 • Letter: #
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•Please highlight where answers are on your document or paper! •Please type or write legible! •Question may be broken up into different pictures!Southern Oll Company produces two grades of gasoline: regular and premium. The profit contributions are $0.30 per galion for regular gasoline and so.5o per galion for premium gasoline. Each gallon of regular gasoline contains 0.3 gllons of grade A crude oil and each gallon of premium gasoline contains 0.6 gallons of grade A crude oll. For the next production period, Southern has 18,000 gallons of grade A crude oil available. The refinery used to produce the gasolines has a production capacity of s0,000 gallons for the next production period. Southern Oil's distributors have indicated that demand for the premium gasoline for the next production period will be at most 20,000 gallons a. Formulate a linear programming model that can be used to determine the number of gallons of regular gasoline and the number of galons of premium gasoline that should be produced in order to maximize total profit contribution. If required, round your answers to two decimal places. Let R number of gallons of regular gasoline produced P number of gallons of premium gasoline produced s.t. Grade A crude oil available Production capacity Demand for premium Numeric field b. What is the optimal solution? Gallons of regular gasoline Gallions of premium gasoline Total profit contributiorn
Explanation / Answer
(a)Maximize 0.30R + 0.50P
Subject to
0.3R + 0.6P <= 18000
R + P <= 50000
P <= 20000
(b)
Optimum Solution
P = 10000
R = 40000
Profit = 17000
(c)
0.3R + 0.6P + s1 = 18000
R + P + s2 = 50000
P + s3 = 20000
s1 = 0 ------ All available crude oil is used
s2 = 0 ------- Production capacity is at its fullest
s3 = 20000 - 10000 = 10000 -------- 10000 premium gasoline have not been used
(d)
Crude oil available 18000
Production Capacity 50000
Demand for premium 10000
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