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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 Programming Given information: Company A produces and sells pet food product packaged under two brand names, Brand X and Brand Y. 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+$35y The profit has to maximize, so the objective function here is Maximize Z = $50x+$35y. Constraints in the problem are Brand X required 5 units of nutrient C and Brand Y requires 4 units of nutrient C. the supply of Nutrient C limited 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 is 5x+4y 33  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. the supply 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 Brand Y is 10x+5y 60  Here the maximum no. of units of Flavor additive available is 60. So this is a maximum constraint. Brand X required 8 units of color additive and Brand Y requires 14 units of color additive. the supply of flavor 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 of Brand Y is 8x+14y 95  Here the maximum no. of units of color additive available is 95. So this is a maximum constraint.

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