Based on Smith (1965). 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 listed in the file P04_108.xlsx. 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 also listed in the same file. For example, if grade 3 germanium is refired, half of the resulting germanium will be grade 3, and the other half will be grade 4. Silvco has sufficient furnace capacity to melt or refire germanium for at most 20,000 transistors per month. Silvco’s monthly demands are for 1000 grade 4 transistors, 2000 grade 3 transistors, 3000 grade 2 transistors, and 3000 grade 1 transistors. Determine how to minimize the cost of producing the needed transistors.
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