Optimization of Profit in Pet Food Production Using Linear Programming
A solved assignment on using linear programming to maximize profitability in pet food production.
David Miller
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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.
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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Operations Management