51 Silicon Valley Corporation (Silvco) manufactures transistors. An important aspect of the manufacture of transistors is the melting of the element germanium (a major component of a transistor) in a furnace. Unfortunately, the melting process yields germanium of highly variable quality.

Two methods can be used to melt germanium; method 1 costs $50 per transistor, and method 2 costs $70 per transistor.

The qualities of germanium obtained by methods 1 and 2 are shown in Table 80. Silvco can refire melted germanium in an attempt to improve its quality. It costs $25 to refire the melted germanium for one transistor. The results of the refiring process are shown in Table 81. Silvco has sufficient furnace capacity to melt or refire germanium for at most 20,000 transistors per month. Silvco’s monthly demands are for 1,000 grade 4 transistors, 2,000 grade 3 transistors, 3,000 grade 2 transistors, and 3,000 grade 1 transistors.

Use linear programming to minimize the cost of producing the needed transistors.

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Incinerator City 1 2 1 30 5 2 36 42 Incinerator 1 2 TABLE 80 59 9 1 Landfill 2 6 86 Grade of Percent Vielded by Melting Melted Germanium Method 1 Method 2 Defective 30 1234 30 20 2 20 25 15 20 4 5 15 22222 20