LP_Graphic_Solution - Ple givea fe se ase w conds be thene...

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Problem Statement Reddy Mikks produces both interior and exterior paints from two raw materials, M1 and M2. Basic data Tons of raw material per ton of Maximumdaily Exterior paint Interior paint availability (tons) Raw material, M1 6 4 24 Raw material, M2 1 2 6 Profit per ton ($1000) 5 4 A market survey indicates that the daily demand for interior paint cannot exceed that of exterior paint by more than 1 ton. Also, the maximum daily demand of interior paint is 2 tons. Reddy wants to determine the optimum (best) product mix of interior and exterior paints that maximizes the total daily profit.
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Equation Form Basic data Tons of raw material per ton of Maximum daily Exterior paint Interior paint availability (tons) Raw material, M1 6 4 24 Raw material, M2 1 2 6 Profit per ton ($1000) 5 4 *Decision variables : Need to determine the amounts to be produced of exterior and interior paints. x 1 = tons produced daily of exterior paint x 2 = tons produced daily of interior paint *Objective (goal) aims to optimize : The company wants to increase its profit as much as possible. z represents thetotal daily profit (in thousands of dollars) Maximize z = 5x 1 + 4x 2 *Constraints: Restrict raw materials usageand demand (Usageof a raw material) (Maximumraw material) by both paints availability 6x 1 + 4x 2 24 ( Raw material M1 ) x 1 + 2x 2 6 ( Raw material M2 ) -x + x 1 (Demand Limit)
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Graphical Method Graph all constraints, including nonnegativity restrictions Solution space consists of infinity of feasible points Identify feasible corner points of the solution space Candidates for the optimum solution are given by a finite number of corner points Use the objective function to determine the optimum corner point from among all the candidates
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Feasible Solution A feasible solution : any values of x 1 and x 2 that satisfy all theconstraints of themodel ThecompleteReddy Mikks model Maximizez = 5x 1 + 4x 2 subject to 3 1 3 1
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Graphical LP Solution Graphical procedureincludes 2 steps Determination: 1) The solution space that defines all feasible solutions of the model 2) The optimum solution from among all the feasible points in the solution space
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