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Look at the slanted line BC, which represents the limit of one of the constraints and runs between the corners B and C. For

 

Look at the slanted line BC, which represents the limit of one of the constraints and runs between the corners B and C. For specificity let point B = (bx,by) and let C = (Cx,Cy). Suppose that the objective function is maximized on the segment BC and that a solution in whole numbers is required. Suppose B = (10, 35.5) and C = (44, 15.35). so you know that the entire feasible region. If the objective function is f(x,y)=3x+5y and x and y are required to be integers, what is the largest value you can get for f in the feasible region?

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