A firm produces an alloy that is made from steel and scrap metal. The cost per ton of steel is $1050 and that of scrap is $820. The technological requirements for the alloy are:

(i) a minimum of one ton of steel is required for every two tons of scrap,

(ii) one hour of processing time is required for each ton of steel and four hours of

processing time for each ton of scrap, and

(iii) the steel and scrap combine linearly to make the alloy. The process loss from steel

is 10% and the loss from scrap is 20%.

Although production may exceed demand, a minimum of 40 tons of the alloy must be manufactured. To maintain efficient plant operation, a minimum of 80 hours of processing time must be used. The supply of both scrap and steel is adequate for the production of the alloy. The objective is to produce the alloy at a minimum cost and answer the following questions based on answer and sensitivity reports

Part a: Are any constraints binding? If so, which one(s)? Part b: If the cost on scarp were changed to $920 a ton, what would the values of the decision

variables be? The objective function?

Part c: If 10 hours less of Processing time were available, what would the values of the decision variables be? The objective function?

Part d: If cost per tons on steel and scrap increased by $100, would the optimal values of the decision variables change? What would the optimal value of the objective function be?