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Author: Admin | 2025-04-28
Vertices.The vertices of this feasible region are:(0,3) (0,4) (2,1) (4,0) and (8,0).Step 4. Substitute the coordinates of the vertices into the objective function.The vertices made up of a pair of coordinates (x, y) and are found at the corners of the feasible region. Substitute the values of x and y from these coordinates into the objective function to find the optimal solution. We will do this ‘simplex process’ for each of the vertices.The objective function is C = 20x + 30y.At (0, 3), x=0 and y=3. The objective function becomes .At (0, 4), x=0 and y=4. The objective function becomes .At (2, 1), x=2 and y=1. The objective function becomes .At (4, 0), x=4 and y =0. The objective function becomes .At (8, 0), x=8 and y=0. The objective function becomes .Step 5. The optimal solution is the vertex at which the minimum value is obtainedIn linear programming, the optimal solution is the maximum or minimum value of the objective function. This is always found at one of the vertices of the feasible region. In this example, we wish to find the combination of supplements that meet the athlete’s needs at the cheapest cost.The cheapest combination was the value which minimised the cost equation.This was at the vertex (2, 1) with a cost of $70.The vertex (2, 1) means that x=2 and y=1.x is the number of supplement A that should be used.y is the number of supplement B that should be used.Therefore, the athlete should use 2 tins of
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