Formulate as a constrained nonlinear program. Clearly indicate the variables, objective function, and constraints.
An engineer at Fertilizer Company has synthesized a sensational new fertilizer made of just two interchangeable basic raw materials. The company wants to take advantage of this opportunity and produce as much as possible of the new fertilizer. The company currently has $40,000 to buy raw materials at a unit price of $8000 and $5000 per unit, respectively. When amounts x1 and x2 of the basic raw materials are combined, a quantity q of fertilizer results given by: q = 4x1 + 2x2 - 0.5x12 - 0.25x22
Part A: Formulate as a constrained nonlinear program. Clearly indicate the variables, objective function, and constraints.
Part B: Solve the Program with Excel Solver (provide exact values for all variables and the optimal objective function).
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