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 Cabbage Number of Acres X X2 X3 Cost (per acre) $320 $128 Profit (per acre) $180 $60 $224 $90 = VI VIII Total 100 $20,000 Z (a) Give the dual problem. Minimize w= 100y+20000y2 subject to: y+320y2 180 Y +128y2 60 1 +224y2 90 with 11 2012 20 (Simplify your answers. Do not factor.) (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 $16149.38 (Type an integer or a decimal.)