Alternate Case Solutions
| bi = Capacity of Resource i | Alternate Case Numbers |
| (See Table 1 for Specifications and Appendices I, II, III for Derivations) |
| Variate Description | Variate Symbol | 1 | 2-A | 2-B | 2-C |
| contribution margin | x0 = | 440b4 | 293.3b1 | 244.44b2 | 73.33b3 |
| gal. of water output | x1 = | 1.5b4 | 1.0b1 | 0.83b2 | 0.25b3 |
| cu. ft. of steam output | x2 = | 1.8b4 | 1.2b1 | 1.00b2 | 0.30b3 |
| k.w.h. of elec. output | x3 = | 6.0b4 | 4.0b1 | 3.33b2 | 1.00b3 |
| units of paper output | x4 = | 1.0b4 | 0.67b1 | 0.56b2 | 0.67b3 |
| cu. ft. of steam purchased | x5 = | 0 | 0 | 0 | 0 |
| slack water capacity (gal.) | s1 = | b1-1.5b4 | 0 | b1-0.83b2 | b1-0.25b3 |
| slack steam capacity (cu. ft.) | s2 = | b2-1.8b4 | b2-1.2b1 | 0 | b2-0.30b3 |
| slack elec. capacity (k.w.h.) | s3 = | b3-6.0b4 | b3-1.4b1 | b3-0.56b2 | 0 |
| unfilled paper demand (units) | s4 = | 0 | b4-0.67b1 | b4-0.56b2 | b4-0.17b3 |
| reciprocal cost of water ($/gal.) | p1 = | 35.46 | 347.5 | 66.65 | 97.89 |
| reciprocal cost of steam ($/cu. ft.) | p2 = | 117.73 | 273.75 | 377.77 | 148.92 |
| reciprocal cost of elec. ($/k.w.h.) | p3 = | 27.66 | 51.11 | 66.69 | 105.93 |
| opportunity value of water ($/gal. of capacity) | y1 = | 0 | 293.33 | 0 | 0 |
| opportunity value of steam ($/cu. ft. of capacity) | y2 = | 0 | 0 | 244.44 | 0 |
| opportunity value of elec. ($/k.w.h. of capacity) | y3 = | 0 | 0 | 0 | 73.33 |
| opportunity value of paper ($/unit of capacity) | y4 = | 440.0 | 0 | 0 | 0 |
| opportunity value of added steam purchase ($/cu.ft.) | y5 = | -82.27 | 73.76 | 177.77 | -51.07 |
| bi = Capacity of Resource i | Alternate Case Numbers |
| (See Table 1 for Specifications and Appendices I, II, III for Derivations) |
| Variate Description | Variate Symbol | 3-A | 3-B | 3-C |
| contribution margin | x0 = | 208b4+155b1 | 301b4+77.3b2 | 73.33b3 |
| gal. of water output | x1 = | 1.00b1 | 0.6b4+0.5b2 | 0.25b3 |
| cu. ft. of steam output | x2 = | -1.20b4+2.00b1 | 1.00b2 | 0.30b3 |
| k.w.h. of elec. output | x3 = | 4.8b4+0.8b1 | 5.28b4+0.4b2 | 1.00b3 |
| units of paper output | x4 = | 1.00b4 | 1.00b4 | 0.67b3 |
| cu. ft. of steam purchased | x5 = | 2.82b4-1.88b1 | 1.692b4-0.94b2 | 0 |
| slack water capacity (gal.) | s1 = | 0 | b1-0.6b4-0.5b2 | b1-0.25b3 |
| slack steam capacity (cu. ft.) | s2 = | b2+1.2b4-2b1 | 0 | b2-0.30b3 |
| slack elec. capacity (k.w.h.) | s3 = | b3-4.8b4-0.8b1 | b3-5.28b4-0.4b2 | 0 |
| unfilled paper demand (units) | s4 = | 0 | 0 | b4-0.17b3 |
| reciprocal cost of water ($/gal.) | p1 = | 200.0 | 45.0 | 97.89 |
| reciprocal cost of steam ($/cu. ft.) | p2 = | 200.0 | 200.0 | 148.92 |
| reciprocal cost of elec. ($/k.w.h.) | p3 = | 40.0 | 40.0 | 105.93 |
| opportunity value of water ($/gal. of capacity) | y1 = | 154.7 | 0 | 0 |
| opportunity value of steam ($/cu. ft. of capacity) | y2 = | 0 | 77.3 | 0 |
| opportunity value of elec. ($/k.w.h. of capacity) | y3 = | 0 | 0 | 73.33 |
| opportunity value of paper ($/unit of capacity) | y4 = | 208.0 | 300.8 | 0 |
| opportunity value of added steam purchase ($/cu.ft.) | y5 = | 0 | 0 | 0 |