Questions: At which point is the function F(x, y) = 3x - 10y maximum when subject to this feasible region? (0,0) Nothing in this list is correct (16,12) (0,20) (0,60) (40,0)

At which point is the function F(x, y) = 3x - 10y maximum when subject to this feasible region? (0,0) Nothing in this list is correct (16,12) (0,20) (0,60) (40,0)
Transcript text: At which point if the function $F(x, y)=3 x-10 y$ maximum when subject to this feasible region? $(0,0)$ Nothing in this list is correct $(16,12)$ $(0,20)$ $(0,60)$ $(40,0)$
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Solution

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Solution Steps

Step 1: Find the Vertices of the Feasible Region

The vertices of the feasible region are given in the graph as (0, 20), (16, 12), (20, 0), and implicitly (0,0). We will test each of these points in the objective function F(x, y) = 3x - 10y.

Step 2: Evaluate the Objective Function at Each Vertex
  • F(0, 20) = 3(0) - 10(20) = -200
  • F(16, 12) = 3(16) - 10(12) = 48 - 120 = -72
  • F(20, 0) = 3(20) - 10(0) = 60
  • F(0,0) = 3(0) - 10(0) = 0
Step 3: Identify the Maximum Value

Comparing the values of the objective function at each vertex, we find that the maximum value is 60, which occurs at the point (20, 0).

Final Answer: The maximum value is achieved at (20,0).

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