A cast-iron foundry is required to produce 1000 lbs. of castings containing at least 0.35 percent…

 A cast-iron foundry is required to produce 1000 lbs. of castings containing at least 0.35 percent manganese and not more than 3.2 percent silicon. Three types of pig iron are available in unlimited amounts, with the following properties

A cast-iron foundry is required to produce 1000 lbs. of castings containing at least 0.35 percent...-1

Assuming that pig iron is melted with other materials to produce cast iron, a linear-programming formulation that minimizes cost is as follows:

A cast-iron foundry is required to produce 1000 lbs. of castings containing at least 0.35 percent...-2

A cast-iron foundry is required to produce 1000 lbs. of castings containing at least 0.35 percent...-3

a) At what cost does pig type A become a candidate for entry into the optimal basis? What activity would it replace?

b) How much can we afford to pay for pure manganese to add to the melt?

 c) How much can the manganese requirement be reduced without changing the basis? What are the values of the other basic variables when this happens?

d) How much can the cost of pig type B change without changing the optimal basis? What are the new basic variables when such a change occurs?

 e) How can the final tableau be optimal if the reduced cost of v1 is −10?

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