Answer:
x = y = 4
Explanation:
A 2-variable linear programming problem is nicely solved by graphing. The solution will be one of the vertices of the solution set. The attached graph shows that means it is one of (x, y) = [(0, 0), (0, 6), (4, 4), (6, 2), (7, 0)}.
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Evaluating the objective function at each of these vertices will show you the solution that maximizes it.
(0, 0) -- P = 40·0 +50·0 = 0
(0, 6) -- P = 40·0 +50·6 = 300
(4, 4) -- P = 40·4 +50·4 = 360
(6, 2) -- P = 40·6 +50·2 = 340
(7, 0) -- P = 40·7 +50·0 = 280
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Additional comment
The solution set would ordinarily be the area that is covered by the shading that signifies the solution set of each of the 5 inequalities. 5 different overlapping shadings can make the graph quite messy, so we have elected to shade the areas that are NOT part of the solution set. In doing so, we have made the boundary lines dashed when they are part of the solution set
The possible solutions are the vertices of the white space on the graph.
The black line on the graph is the line corresponding to the maximum value of the objective function. To maximize the objective function, we want that line as far from the origin as possible. It is shown intersecting the vertex of the solution space that meets that condition.