# [Excel spreadsheet available at http://web.mit.edu/15.053/www/Exer3.10.xls] The Reclamation…

[Excel spreadsheet available at http://web.mit.edu/15.053/www/Exer3.10.xls] The Reclamation Machining Company makes nuts and bolts from scrap material supplied from the waste products of three steel-using firms. For each 100 pounds of scrap material provided by firm A, 10 cases of nuts and 4 cases of bolts can be made, with a contribution of \$46. 100 pounds from firm B results in 6 cases of nuts, 10 cases of bolts, and a contribution of \$57. Use of 100 pounds of firm C’s material will produce 12 cases of nuts, 8 of bolts, and a contribution of \$60. Assuming Reclamation can sell only a maximum of 62 cases of nuts and 60 of bolts, the final tableau for a linear-programming solution of this problem is as follows:

a) What is the optimal solution?

b) Is the solution unique? Why?

c) For each of the three sources, determine the interval of contribution for which the solution in part (a) remains optimal.

d) What are the shadow prices associated with the optimal solution in (a), and what do they mean?

e) Give an interval for each sales limitation such that the shadow prices in (d) remain unchanged.

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