Optimization and Brand Essay - 836 Words

Answers are hi-lighted yellow. Company As nationally advertised brand is Brand X. Contribution to profit with Brand X is $40 per case. Company As re-proportioned formula is sold under a private label Brand Y. Contribution to profit with Brand Y is $30 per case. Company As 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. TheShow MoreRelatedThe Top 10 Benefits Of Seo Essay706 Words   |  3 PagesSearch Engine Optimization Can Help Your Website Far gone are days of using the Yellow Pages or other â€Å"offline† directories as a cost effective means of advertising. As a result, businesses are investing heavily in Search Engine Optimization to gain an edge over their competition in Search Engine rankings. More and more companies are gaining online exposure to reach wider audiences and to increase their market share. As far as internet marketing is concerned, Search Engine Optimization, or SEO, isRead MoreDifference Between Inbound And Outbound Marketing Essay1136 Words   |  5 PagesExplain the difference between inbound and outbound marketing. 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