Qat1 Task 39.3.1-03,11,12

696 Words3 Pages
ANSWER A: Nutrients C Flavor Color ANSWER A 1: NUTRIENTS: Brand X and Brand Y both require a minimum of 4 units of Nutrients C per case and the maximum units of Nutrient C that can be produced per production is 30 units. FLAVOR ADDITIVE: Brand X requires a minimum of 12 units of flavor additive per case and the maximum Flavor additive that can be used per production is 72 units. Brand Y requires 6 units of flavor additive per case and the maximum Flavor additive that can be used per production is 72 units. 4 X + 4 Y ≤ 30 12 X + 6 Y ≤ 72 6 X + 15 Y ≤ 90 COLOR: Brand X requires a minimum of 6 units of Color per case and the maximum Color per production is 90 units. Brand Y requires 15 units of Color per case and the maximum Color per productions is 90 units. Nutrients C 4 X + 4 Y ≤ 30 (0, 7.5) 4(0) + 4 Y ≤ 30 4 Y ≤ 30 4 Y ≤ 30 4 4 Y ≤ 7.5 (7.5, 0) 4 X + 4 (0) ≤ 30 4 X ≤ 30 4X ≤ 30 4 4 X ≤ 7.5 Flavor 12 X + 6 Y ≤ 72 (0, 12) 12(0) + 6 Y ≤ 72 6 Y ≤ 72 6 Y ≤ 72 6 6 Y ≤ 12 Color 6 X + 15 Y ≤ 90 (0, 6) 6 (0) + 15 Y ≤ 90 15 Y ≤ 90 15 Y ≤ 90 15 15 Y≤6 (15, 0) 6 X + 15 (0) ≤ 90 6 X ≤ 90 6 X ≤ 90 6 6 X ≤ 15 (6, 0) 12 X + 6(0) ≤ 72 12 X ≤ 72 12 X ≤ 72 12 12 X≤6 ANSWER B: Profit = $40 X + $30 Y The Y intercept of 0, 8 yields a profit of $30(8) = $240 The X intercept of 6, 0 yields a profit of $40(6) =$240 ANSWER C: I found the answer to part C by first finding the vertices of the feasible region, where we can produce given our restraints. From the graph the nutrients cannot be greater than 6 cases therefore that gave me the first corner (0, 6). The next corner is located where color and nutrients intersect at (2.5, 5). The third corner was where the flavor intersected with nutrients (4.5, 3). The fourth corner (6, 0) due to the available amount of nutrients and the last corner is (0, 0). See below graph where I inserted black lines to outline the

More about Qat1 Task 39.3.1-03,11,12

Open Document