A farmer has 100 acres of available land and $20,000 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 X $160 $60 Number of Acres Cost (per acre) Profit (per acre) (a) Give the dual problem. Minimize subject to: with x $400 $180 w-100 y +20000 y+40022180 Y+1602260 Y 2002 200 20.20 S Cabbage x $280 S $90 m Total 100 $20,000 2 (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 90 acres but capital increases to $21,000. The farmer's estimated profit is $ (Simplify your answer.) (c) Suppose the farmer has 110 acres of land but only $19,000. Find the optimum profit and the planting strategy that will produce this profit. acres of com, and acres of cabbage will produce an optimal profit of $ Planting acres of potatoes, (Simplify your answers.) O 5