Explain why you cannot conclude that optimal solutions exist without graphing the objective function. for various feasible solutions. Graph the feasible region and use graphs of the objective function for various values of z to determine the maximum value and the minimum value, if they exist Minimize and maximize zax-y Subject to x-2y 20 2x-y 26 xyzo Why can you not conclude that optimal solutions exist? OA. Neither a maximum value nor a minimum value exist OB. The feasible region is unbounded and one of the coeficients of the objective function is negative OC. The feasible region is empty and one of the coefficients of the objective function is negative OD. The feasible region is bounded and one of the coefficients of the objective function is negative

A farmer has 500 acres of available land and $100,000 to spend. He wants to plant the combination of crops which maximizes his profit. Complete parts (a) through (c). Profits and Constraints for Crops Potatoes Corn Number of Acres Cost (per acre) Profit (per acre) X₁ $320 $120 with Minimize subject to: y₁ +320y₂ 2 120. Y₁+1282 2 40 w = 500 y₁ + 100000 ₂ Y₁+224y > 60 Y₁ 20, y₂ 20 $128 $40 The farmer's estimated profit is $ (Simplity your answer.) Cabbage X3 $224 $60 S ≤ = Total 500 $100,000 Z (b) The solution to the dual problem can be interpreted as shadow profits. Use shadow profits to estimate the farmer's profit if land is cut to 400 acres but capital increases to $110,000.

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