A nutrition center sells haelth food to mountain climbing teams. The trailblazer mix package contains 1 pound of corn cereal mixed with 4 pounds of wheat cereal.The frontier mix package contains 2 pounds of corn cereal mixed with 3 pounds of wheat cereal.The center has 30 pounds of corn cereal and 60 pounds of wheat cereal available to use. define variables. write inequalities to represent the problem.
To define the variables for this problem, we can use:
Let x = the number of Trailblazer mix packages
Let y = the number of Frontier mix packages
Now, let's write the inequalities for the given constraints:
1) Corn cereal constraint: The total weight of corn cereal used in both mix packages should not exceed the available amount of 30 pounds. We can write this as:
1x (weight of corn cereal in a Trailblazer mix package) + 2y (weight of corn cereal in a Frontier mix package) ≤ 30
2) Wheat cereal constraint: The total weight of wheat cereal used in both mix packages should not exceed the available amount of 60 pounds. We can write this as:
4x (weight of wheat cereal in a Trailblazer mix package) + 3y (weight of wheat cereal in a Frontier mix package) ≤ 60
3) Non-negativity constraint: The number of packages cannot be negative, so we add the following constraint:
x ≥ 0 (number of Trailblazer mix packages)
y ≥ 0 (number of Frontier mix packages)
These inequalities represent the problem's constraints.