# [Excel spreadsheet available at http://web.mit.edu/15.053/www/Exer3.14.xls] The Classic Stone…

[Excel spreadsheet available at http://web.mit.edu/15.053/www/Exer3.14.xls] The Classic Stone Cutter Company produces four types of stone sculptures: figures, figurines, free forms, and statues. Each product requires the following hours of work for cutting and chiseling stone and polishing the final product:

The last row in the above table specifies the contribution to overhead for each product. Classic’s current work force has production capacity to allocate 300 hours to cutting, 180 hours to chiseling, and 300 hours to polishing in any week. Based upon these limitations, it finds its weekly production schedule from the linear-programming solution given by the following tableau

a) Determine a range on the cutting capacity such that the current solution remains optimal.

b) Busts have the following characteristics:

Cutting                             15 hrs.

Chiseling                           10 hrs.

Polishing                           20 hrs.

Contribution/unit            \$240

Should Classic maintain its present line or expand into busts?

c) Classic can buy 5 hours of cutting capacity and 5 hours of chiseling capacity from an outside contractor at a total cost of \$75. Should Classic make the purchase or not?

d) By how much does the contribution from free forms have to be increased to make free forms profitable to produce?

e) Give a range on the contribution from figures such that the current solution remains optimal. What activities enter the basis at the bounds of this range?

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