QUESTION

A gold processor has two sources of gold ore, source A and source B. In order to keep his plant running, at least three tons of ore must be processed each day. Ore from source A costs $20 per ton to process, and ore from source B costs $10 per ton to process. Costs must be kept to less than $80 per day. Moreover, Federal Regulations require that the amount of ore from source B cannot exceed twice the amount of ore from source A. Ore from source A yields 2 oz. of gold per ton and ore from source B yields 3 oz. of gold per ton.

(a) Formulate the problem that will maximize the amount of gold extracted as a linear programming problem, defining the decision variables, constraints and objective function carefully.

(b) Plot the constraints lines for this linear programming problem by drawing a neat graph indicating the feasible region, R clearly on your graph

(c) Determine the feasible corner point (X) at which the optimal solution to this problem is achieved. Hence, determine how many tons of ore from both sources must be processed each day to maximize the amount of gold extracted subject to the above constraints

(d) Briefly outline the limitations of LP