QAT 1 TASK 2 Solution
Company A produces and sells a popular pet food product packaged under two brand names, with formulas that contain different proportions of the same ingredients. Company A made this decision so that their national branded product would be differentiated from the private label product. Some product is sold under the company’s nationally advertised brand (Brand Y), while the re-proportioned formula is packaged under a private label (Brand X) and is sold to chain stores.

Because of volume discounts and other stipulations in the sales agreements, the contribution to profit from the Brand Y product sold to distributors under the company’s national brand is only $12.50 per case compared to $100 per case for private label product Brand X. There are four ingredients involved in this problem. The recipes specifying the use of each ingredient in the two product brands are given in the template. Also note, an ingredient may either be in limited supply or may have government regulations requiring a minimum or maximum amount of an ingredient.

Objective A
The constraint for nutrient C = 4x+4y is less or equal than 30 which is the minimum constraint. Therefore y<=-x+7.5 is the maximum constraint.
The constraint for flavor additive = 12x+6y is less or equal than72 which is the minimum constraint.. Therefore y<=-2x+12 is the maximum constraint.
The constraint for color additive = 6x+15y is less or equal than 90 which is the minimum constraint.
Therefore y<=-2x/5+6 is the maximum constraint.
Objective B
.Objective function (P) is (P) = $40x+$30y
Objective C
The vertices are:
P(0, 0) = $0 + $0 = $0 profit
P(0, 6) = $0 + $ 180 = $180 profit
P(2.5, 5) = $100 + $150 = $250 profit
P(4.5, 3) = $180 + $90 = $270 profit
P(6, 0) = $240 + $0 = $240 profit
Therefore the company should produce 4.5 cases of brand X and 3 cases of brand Y in