intro management science

Problem 3.19 marks in total) An iron foundry has a firm order to produce 1000 pounds of casting containing at least 0.45 percent manganese and between 3.25 percent and 5.50 percent silicon. As these particular castings are a special order, there are no suitable castings on hand. The castings sell for S0.45 per pound. The foundry has three types of pig iron available in essentially unlimited amounts, with the following properties Type of pig iron M. Further, the production process is such that pure manganese can also be added directly to the melt. The costs of the various possible inputs are It costs 0.5 cents to melt down a pound of pig iron A possible formulation of this problem is given as follows: Decision variables: * -Pounds of pig iron A. * -Pounds of pig iron B * -Pounds of pig iron, * -Pounds of pure manganese 23:40:43,048 KRAT 00.00 CORE, 0.0045, The problem has been solved with a software, which outputted the following results (1 mark) What is the optimal value of the problem? (2 marks) What is the optimal solution obtained by the software? si(2 marks) Interpret the reduced cost associated with the variable 40 (2 marks) What are the binding comstraints? Please, justify your answers. (2 marks) What would be the effect on the objective value (optimal profit) if one additional pound of castings were ordered? Please, explain your answers 2