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QAT1 Task 2: Competency 309.3.1-03, 11, 12

Determine the equations for each of the three constraints.

Nutrient C : 4x + 4y ≤ 30

Flavor A : 12x + 6y ≤ 72

Color : 6x + 15y ≤ 90

Identify each constraint as Minimum or Maximum.

Nutrient C constraint is a Maximum

Flavor A constraint is a Maximum

Color is a Maximum

Determine the total contribution to profit that lies on the Object Function as plotted on the graph.

By visual observation the objective function line indicates shows Brand X = 3 and Brand Y = 4.

Using these values and the objective function of 30y + 40x = 30*4 +40*3 = 240

Determine how many cases of each type should be produced to generate the greatest profit.

Solving for the intersection of Color (4x + 4y = 30) and Nutrient (6x + 15y = 90) yields the values of Y = 5 case and X = 2.5 cases for a total of 7.5 Cases.

Entering these values into the objective function:

30y + 40x = 30*5 + 40*2.5 = 250

Solving for the intersection of Flavor (12x + 6y = 72) and Color (4x + 4y = 30) yields the values of Y = 3 and X = 4.5 cases for a total of 7.5 cases.

Entering these values into the objective function:

30y + 40x = 30*3 + 40*4.5 = 270

Solving for the intersection Flavor (12x + 6y = 72) and Nutrient (6x + 15y = 90) yields the values of Y = 4.5 and X =3.75 for a total of 8.25 cases.

Entering these values into the objective function:

30y + 40x = 30*4.5 + 40*3.75 = 285

Determine the total contribution to profit that would be generated by the production level you recommend in part C.

Using the values obtained from the intersection of Flavor and Nutrient where X =3.75 and Y = 4.5 generates expected profit:

30y + 40x = 30*4.5 + 40*3.75 =…...

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