$\mathrm{x}\ge 0,\mathrm{y}\ge 0, \mathrm{x}+\mathrm{y} \le 5, \mathrm{x}+2\mathrm{y}\ge 8$ শর্তানুসারে z = 2x-y এর সর্বনিম্ন মান -

The problem involves finding the minimum value of the expression z = 2x - y under the constraints given by the inequalities:

    
• x ≥ 0
    
• y ≥ 0
    
• x + y ≤ 5
    
• x + 2y ≥ 8

To determine the minimum value of z, we need to evaluate the feasible region formed by these constraints.

1. The inequality x + y ≤ 5 indicates that the points satisfying this condition lie below or on the line y = 5 - x.

2. The inequality x + 2y ≥ 8 indicates that the points satisfying this condition lie above or on the line y = (8 - x)/2.

Next, we find the intersection points of these lines with the axes and determine feasible points that satisfy all constraints. After evaluating the corner points of the feasible region formed by these lines, we can substitute these points into the equation for z to find its minimum value.

By testing the possible points, it is found that at a certain point which meets all the conditions, the minimum value of z is indeed -5, which is the correct answer among the given options.

In summary, the answer -5 is correct because it is the minimum output of the objective function z = 2x - y when evaluated at the valid corner points determined by the constraints.

AI-এর ব্যাখ্যায় ভুল থাকতে পারে।