A fertilizer plant can make a product by any of 3 processes. Using decision variables xj !number of units produced by process j, the following linear program computes a minimum cost way to produce 150 units with available resources:

min 15x1 + 11x2 + 18x3 s.t. x1 + x2 + x3 = 150 2x1 + 4x2 + 2x3 … 310 4x1 + 3x2 + x3 … 450 x1, x2, x3 Ú 0

(a) Explain why this LP implicitly assumes that objective function coefficients are variable costs.

(b) Use class optimization software to solve the given LP.

(c) Formulate a revised ILP model implementing a requirement that only one of the 3 activities may be used.

(d) Use class optimization software to solve the ILP of part (c).

(e) Formulate a different revised ILP implementing a fixed setup cost of 400 charged for each activity used at all.

(f) Use class optimization software to solve the ILP of part (e).

(g) Formulate another revised ILP implementing a requirement that an activity can be used only if a minimum of 50 units are produced.

(h) Use class optimization software to solve the ILP of part (g).