The Tall Tree lumber company owns 95,000 acres of forestland in the Pacific northwest, at least 50,000 of which must be aerially sprayed for insects this year. Up to 40,000 acres could be handled by planes based at Squawking Eagle, and up to 30,000 acres could be handled from a more distant airstrip at Crooked Creek. Flying time, pilots, and materials together cost $3 per acre when spraying from Squawking Eagle and $5 per acre when handled from Crooked Creek. Tall Tree seeks a minimum cost spraying plan.

(a) Formulate a mathematical programming model to select an optimal spraying plan using decision variables x1! thousands of acres sprayed from Squawking Eagle and x2! thousands of acres sprayed from Crooked Creek.

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

(c) Using a 2-dimensional plot, solve your model graphically for an optimal spraying plan, and explain why it is unique.

(d) On a separate 2-dimensional plot, show graphically that the problem is unbounded if the Squawking Eagle capacity and both nonnegativity constraints are omitted.

(e) On a separate 2-dimensional plot, show graphically that the problem becomes infeasible if the Crooked Creek facility is destroyed by fire.