Business, 18.04.2021 01:10 khanhlan7213

Southern Oil Company produces two grades of gasoline: regular and premium. The profit contributions are $0.30 per gallon for regular gasoline and $0.50 per gallon for premium gasoline. Each gallon of regular gasoline contains 0.3 gallons of grade A crude oil and each gallon of premium gasoline contains 0.6 gallons of grade A crude oil. 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 50,000 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 gallons 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
- Select your Answer -MaxMinItem 1 R + P
s. t.
R + P - Select your Answer -??=Item 6 Grade A crude oil available
R + P - Select your Answer -??=Item 10 Production capacity
P - Select your Answer -??=Item 13 Demand for premium
R, P - Select your Answer -??=Item 15
(b) What is the optimal solution?
Gallons of regular gasoline
Gallons of premium gasoline
Total profit contribution $
(c) What are the values and interpretations of the slack variables?
Constraint Value of Slack Variable
Interpretation
1 - Select your Answer -All available grade A crude oil is usedAll available grade A crude oil is not usedItem 21
2 - Select your Answer -Total production capacity is usedTotal production capacity is not usedItem 23
3 - Select your Answer -Premium gasoline production is 10,000 gallons less than the maximum demandPremium gasoline production is 10,000 gallons greater than the maximum demandItem 25
(d) What are the binding constraints?
Grade A crude oil available - Select your Answer -BindingNon-bindingItem 26
Production capacity - Select your Answer -BindingNon-bindingItem 27
Demand for premium - Select your Answer -BindingNon-bindingItem 28

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Southern Oil Company produces two grades of gasoline: regular and premium. The profit contributions...