Sun Agriculture (SunAg) operates a farm of 10,000 acres in the dry southwestern part of the United States. In the next season SunAg can plant acres in either vegetables, which return a profit of approximate $450 per acre, or cotton, which returns

$200 per acre. As a precaution against bad weather, insects, and other factors, SunAg will plant no more than 70% of its total holdings in any one of these options. Also, irrigation water is limited. To grow vegetables requires 10 units (of water) per acre, and cotton requires 7, out of a government allocation of 70,000 units per season. SunAg wishes to develop a planting plan that maximumes profit.

(a) Formulate a mathematical programming model to solve SunAg’s problem using 2 main constraints, 2 upper bound constraints, 2 variable-type constraints, and decision variables v = acres in vegetables and c = acres in cotton.

(b) Enter and solve your model with the class optimization software.

(c) Using a 2-dimensional plot, find an optimal plan graphically.

(d) Show graphically that if we accidentally omitted the upper and lower bound constraints on the two variables, the resulting model would be unbounded.

(e) Now return to the correct model and imagine that SunAg is required by government regulation to plant all its acres. Show graphically that this case is infeasible.