Question

Seastrand Oil Company produces two grades of gasoline: regular and high octane. Both gasolines are produced by blending two types of crude oil. Although both types of crude oil contain the two important ingredients required to produce both gasolines, the percentage of important ingredients in each type of crude oil differs, as does the cost per gallon. The percentage of ingredients A and B in each type of crude oil and the cost per gallon are shown.

Crude Oil   Cost   Ingredient A   Ingredient B
1   $0.10   20%   60%
2   $0.15   50%   30%
Each gallon of regular gasoline must contain at least 40% of ingredient A, whereas each gallon of high octane can contain at most 50% of ingredient B. Daily demand for regular and high-octane gasoline is 900,000 and 700,000 gallons, respectively. How many gallons of each type of crude oil should be used in the two gasolines to satisfy daily demand at a minimum cost? Round your answers to the nearest whole number. Round the answers for cost to the nearest dollar.

gallons of crude 1 used to produce regular   =  
gallons of crude 1 used to produce high-octane   =  
gallons of crude 2 used to produce regular   =  
gallons of crude 2 used to produce high-octane   =  
Cost   =   $

Answer 1

ANSWER:-

Calculate the number of gallons of each type of "crude oil" using the following methodology, as shown below: Step-1: Decide the decision variables: Let, x -Gallons of crude oil of type-1 required to produce regular gasoline X1 -Gallons of crude oil of type-1 required to produce High octane gasoline X1 -Gallons of crude oil of type-2 required to produce regular gasoline x2 -Gallons of crude oil of type-2 required to produce High octane gasoline Step-2: Formulate the objective function: The objective is to minimize cost. Write this in mathematical form as shown below: Minimizecost(Z)- Cost Minimizecost(Z)-0.1(x0.15(xi +Xn) Step-3: Set up constraints: Regular gasoline must contain at least 40% of ingredient A 20.5x 204( after solvingitreduces to>>0.2x+0.1x, 20 High octane gasoline can contain at most 50% of ingredient B 0.6x 0.3x, 50.5(xn +X) After solvingitreduces to >>0.1xn -0.2xn <0 Demand constraints +X, 2 800,000 x2x 2 500,000 Non negativity constraints 2 0

Solve using solver as shown below: Enter data in excel and solver, as shown below, and click on solve Decision variables 2 Crude Oil Cost High Octane 0.1 0 0.15 Constraints 2800000 Demand 2 500000 Demand 10 D3+D4 12 13 14 (C3+D3)*B3(C4+D4) B4 Objective function Solver Parameters Set Objective: To: Ry Changing Variable Cels: Subject to the Constraints: Reset Al Make Unconstrained Variables Non-Negative Sglect a Solving Method: Simplex LP Solving Method Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear. Select the LP Simplex engine for linear Solver Problems, and select the Evolutionary engine for Solver problems that are

The result of the solver is shown below: Decision variables Crude Oil Cost Regular High Octane 0.1 266,666.67333,333.33 0.15 533,333.33166,666.67 Constraints 0 Forty percent Fifty percent 000 Demand Obje ctive function $165,000.00 The minimum cost is S165,000 at purchasing 266,666.67 + 333,333.33 600,000 eallons of crude oil- 1 and 533.33.3+166.66 crude oil 2. 66.67 700,000 gallons of

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