Optimization of Profit in Pet Food Production Using Linear Programming

A solved assignment on using linear programming to maximize profitability in pet food production.

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Optimization of Profit in Pet Food Production Using Linear ProgrammingGiven information:Company A produces and sells pet food product packaged under two brand names, Brand X and BrandY.Profit on Brand X is $50 and Brand Y is $35.Let ‘x’ be the number of Brand X items sold and ‘y’ be the number of Y brand items sold.Then the profit is = $50x+$35yThe profit has to maximize, so the objective function here isMaximize Z = $50x+$35y.Constraints in the problem areBrand X required 5 units of nutrient C and Brand Y requires 4 units of nutrient C. the supply of Nutrient Climited to 33 units.The no.of units of C required to produce x no.of units of Brand X and y no.of units of Brand Y is5x+4y33Here the maximum no. of units of C available is 33. So this is a maximum constraint.Similarly,Brand X required 10 units of flavor additive and Brand Y requires 5 units of flavor additive. thesupply of flavor additive limited to 60 units.The no.of units of flavor additive required to produce x no.of units of Brand X and y no.of units of BrandY is10x+5y60Here the maximum no. of units of Flavor additive available is 60. So this is a maximum constraint.Brand X required 8 units ofcolor additive and Brand Y requires 14 units of color additive. the supply offlavor additive limited to 95 units.Next, the no.of units of color additive required to produce x no.of units of Brand X and y no.of units ofBrand Y is8x+14y95Here the maximum no. of units of color additive available is 95. So this is a maximum constraint.

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Operations Management

Optimization of Profit in Pet Food Production Using Linear Programming

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