Optimization and Brand Essay

836 WordsSep 26, 20144 Pages
Answers are hi-lighted yellow. Company A's nationally advertised brand is Brand X. Contribution to profit with Brand X is $40 per case. Company A's re-proportioned formula is sold under a private label Brand Y. Contribution to profit with Brand Y is $30 per case. Company A's objective is to maximize the total contribution to profit. Three constraints limit the number of cases of Brand X and Brand Y that can be produced. Constraint 1: The available units of nutrient C (n) is 30. Constraint 2: The available units of flavor additive (f) is 72. Constraint 3: The available units of color additive (c) is 90. Material units per case of Brand X and Brand Y: Product Brand X Brand Y Formula for a case of Brand X = 4n+12f+6c Nutrient C:…show more content…
The other two extreme points must be solved using both line equations simultaneously: Of the five extreme points, one point will provide the maximum profit contribution. Solving for the extreme point where the color and nutrient lines intersect subtract the two equations: 1) 6X + 15Y = 90 Multiply this equation by 2 to eliminate the X variable 4X + 4Y = 30 Multiply this equation by 3 to eliminate the X variable 2) 12X + 30Y = 180 12X + 12Y = 90 Subtract equation two from equation one 18Y = 90 Y = 5 Substituting Y = 5 back into the first equation 6X + 15(5) = 90 6X + 75 = 90 6X = 15 X = 2.5 Extreme point = (2.5,5) Solving for the extreme point where the flavor and nutrient lines intersect subtract the two equatitions: 1) 12X + 6Y = 72 4X + 4Y = 30 Multiply this equation by 3 to eliminate the x variable 2) 12X + 6Y = 72 Subtract equation two from equation one 12x + 12y = 90 -6Y = -18 Y = 3 Substituting Y = 3 back into the first equation 12X + 6(3) = 72 12X + 18 = 72 12X = 54 X = 4.5 Extreme point = (4.5,3) B. Determine the total contribution to profit if the company produces a combination of cases of Brand X and Brand Y that lies on the purple objective function (profit line) as it is plotted on "Graph 1". The
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