The minimum value of c = 7x + 8y is 42. The minimum value is obtained at point (6, 0).
To calculate the minimum value of the given equation w.r.t the given constraints(inequalities), the steps are:
Step 1: Identify the system of inequalities in the given constraints
Step 2: Graph those inequalities
Step 3: Identify the maximum and minimum values of x and y that satisfy the given inequalities
Step 4: Then, with the obtained coordinates solve the given equation to get the minimum value.
The given equation is C = 7x + 8y, and the constraints list is
2x + y ≥ 0
x + y ≥ 6
x ≥ 0
y ≥ 0
Graphing these inequalities and shading the region that satisfies the given inequalities.
So, from the graph,
the x-values that satisfy all the given inequalities are [6, ∞]
the y-values that satisfy all the given inequalities are [0, ∞]
So, the required coordinate is (6, 0). By this, we can calculate the minimum value of the given equation C = 7x + 8y
Then,
C = 7(6) + 8(0) = 42 + 0 = 42
Thus, the minimum value of the given equation is 42.
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Disclaimer: The given question is incomplete. Here is the complete question.
Question: What is the minimum value of c = 7x 8y, given the constraints on x and y listed below?
2x + y ≥ 0
x + y ≥ 6
x ≥ 0
y ≥ 0
