3. In one study of the quantities x and y of natural gas that Western Europe...

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3. In one study of the quantities x and y of natural gas that Western Europe should import from Norway and Siberia, respectively, it was assumed that the benefits were given by the function f(x, y)=9x+8y- 6(x + y)² Because of capacity constraints, x and y must satisfy 0≤ x ≤ 5 and 0≤ y ≤ 3. Finally, for political reasons, it was felt that imports from Norway should not provide too small a fraction of total imports at the margin, so that x ≥ 2(y – 1), or equivalently -x+2y ≤ 2. In the xy-plane, draw the set S of all points satisfying the three constraints, and then find the quantities that maximize the benefits, subject to the three constraints. 3. In one study of the quantities x and y of natural gas that Western Europe should import from Norway and Siberia, respectively, it was assumed that the benefits were given by the function f(x, y)=9x+8y- 6(x + y)² Because of capacity constraints, x and y must satisfy 0≤ x ≤ 5 and 0≤ y ≤ 3. Finally, for political reasons, it was felt that imports from Norway should not provide too small a fraction of total imports at the margin, so that x ≥ 2(y – 1), or equivalently -x+2y ≤ 2. In the xy-plane, draw the set S of all points satisfying the three constraints, and then find the quantities that maximize the benefits, subject to the three constraints.

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SOLUTION Okay here are the steps to solve this problem 1 Draw the constraints graphically in th... View the full answer