• VVA firm operates four farms of comparable productivity. Each farm has a certain amount of usable acreage and a supply of labor hours to plant and tend the crops. The data for the upcoming season are shown in the following table.

  Farm

  Usable Acreage

  Labor hours available per month

  $1$

  $500$

  $1700$

  $2$

  $900$

  $3000$

  $3$

  $300$

  $900$

  $4$

  $700$

  $2200$

  The organization is considering three crops for planting.

  These crops differ primarily in their expected profit per acre and in the amount of labor they require, as shown in the following table,

  Crop

  Maximum Acreage

  Monthly labor hours required per acre

  Expected profit per acre$($$$)$

  A

  $700$

  $2$

  $500$

  B

  $800$

  $4$

  $200$

  C

  $300$

  $3$

  $300$

  thermore, the total acreage that can be devoted to any particular crop is limited by the associated requirements for harvesting equipment.

  In order to maintain a roughly uniform workload among the farms, management$’$s policy is that the percentage of usable acreage planted must be the same at each farm.

  However, any combination of the crops may be grown at any of the farms as long as all constraints are satisfied $($including the uniform workload requirement.$)$

  Management wishes to know how many acres of each crop should be planted at the respective farms in order to maximize expected profit. Formulate this as a linear programming model.